Search results for: complex nonlinear system.

Authors: Martin Cermak, Stanislav Sysala

Abstract:

In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MatLab.

Keywords: Isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution.

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Authors: M.M. Namazi, S.M. Saghaiannejad, A. Rashidi

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In this paper by using the port-controlled Hamiltonian (PCH) systems theory, a full-order nonlinear controlled model is first developed. Then a nonlinear passivity-based robust adaptive control (PBRAC) of switched reluctance motor in the presence of external disturbances for the purpose of torque ripple reduction and characteristic improvement is presented. The proposed controller design is separated into the inner loop and the outer loop controller. In the inner loop, passivity-based control is employed by using energy shaping techniques to produce the proper switching function. The outer loop control is employed by robust adaptive controller to determine the appropriate Torque command. It can also overcome the inherent nonlinear characteristics of the system and make the whole system robust to uncertainties and bounded disturbances. A 4KW 8/6 SRM with experimental characteristics that takes magnetic saturation into account is modeled, simulation results show that the proposed scheme has good performance and practical application prospects.

Keywords: Switched Reluctance Motor, Port HamiltonianSystem, Passivity-Based Control, Torque Ripple Minimization

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Authors: Osama A. Marzouk

Abstract:

We propose a reduced-ordermodel for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform timeconsuming simulations and solving the partial differential equations (PDEs) governing the flow field.

Keywords: reduced-order model, wake oscillator, nonlinear, ODEsystem

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

Abstract:

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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Authors: Mohammed A. Hajeeh

Abstract:

This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.

Keywords: Repairable models, imperfect, availability, exponential distribution.

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Authors: Yoonjung An, Yongtae Park

Abstract:

Offering a Product-Service System (PSS) is a well-accepted strategy that companies may adopt to provide a set of systemic solutions to customers. PSSs were initially provided in a simple form but now take diversified and complex forms involving multiple services, products and technologies. With the growing interest in the PSS, frameworks for the PSS development have been introduced by many researchers. However, most of the existing frameworks fail to examine various relations existing in a complex PSS. Since designing a complex PSS involves full integration of multiple products and services, it is essential to identify not only product-service relations but also product-product/ service-service relations. It is also equally important to specify how they are related for better understanding of the system. Moreover, as customers tend to view their purchase from a more holistic perspective, a PSS should be developed based on the whole system’s requirements, rather than focusing only on the product requirements or service requirements. Thus, we propose a framework to develop a complex PSS that is coordinated fully with the requirements of both worlds. Specifically, our approach adopts a multi-domain matrix (MDM). A MDM identifies not only inter-domain relations but also intra-domain relations so that it helps to design a PSS that includes highly desired and closely related core functions/ features. Also, various dependency types and rating schemes proposed in our approach would help the integration process.

Keywords: Inter-domain relations, intra-domain relations, multi-domain matrix, product-service system design.

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Authors: Chidentree Treesatayapun

Abstract:

A direct adaptive controller for a class of unknown nonlinear discrete-time systems is presented in this article. The proposed controller is constructed by fuzzy rules emulated network (FREN). With its simple structure, the human knowledge about the plant is transferred to be if-then rules for setting the network. These adjustable parameters inside FREN are tuned by the learning mechanism with time varying step size or learning rate. The variation of learning rate is introduced by main theorem to improve the system performance and stabilization. Furthermore, the boundary of adjustable parameters is guaranteed through the on-line learning and membership functions properties. The validation of the theoretical findings is represented by some illustrated examples.

Keywords: Neuro-Fuzzy, learning algorithm, nonlinear discrete time.

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Authors: Mai S. Mabrouk, Nahed H. Solouma, Abou-Bakr M. Youssef, Yasser M. Kadah

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Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of real sequences encoded into a time series using EIIP sequence indicators. In order to discriminate between coding and non coding DNA regions, the phase space trajectory was first reconstructed for coding and non-coding regions. Nonlinear dynamical features are extracted from those regions and used to investigate a difference between them. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between coding (CR) and non-coding regions (NCR) in DNA sequences. Finally, the classifier is tested on real genes where coding and non-coding regions are well known.

Keywords: Gene prediction, nonlinear dynamics, correlation dimension, Lyapunov exponent.

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Authors: Meng Hu, Lili Wang

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In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.

Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.

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Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue

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A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.

Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.

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Authors: Youguo Wang, Lenan Wu

Abstract:

Stochastic resonance (SR) is a phenomenon whereby the signal transmission or signal processing through certain nonlinear systems can be improved by adding noise. This paper discusses SR in nonlinear signal detection by a simple test statistic, which can be computed from multiple noisy data in a binary decision problem based on a maximum a posteriori probability criterion. The performance of detection is assessed by the probability of detection error Per . When the input signal is subthreshold signal, we establish that benefit from noise can be gained for different noises and confirm further that the subthreshold SR exists in nonlinear signal detection. The efficacy of SR is significantly improved and the minimum of Per can dramatically approach to zero as the sample number increases. These results show the robustness of SR in signal detection and extend the applicability of SR in signal processing.

Keywords: Probability of detection error, signal detection, stochastic resonance.

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Authors: Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad, Israr Ahmad

Abstract:

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.

Keywords: Nonlinear Active Control, Chen and Tigan Chaotic systems, Lyapunov Stability theory, Synchronization.

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Authors: Hoda Aleali, Nastaran Mansour, Maryam Mirzaie

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In this paper, we study the optical nonlinearities of Silver sulfide (Ag2S) nanostructures dispersed in the Dimethyl sulfoxide (DMSO) under exposure to 532 nm, 15 nanosecond (ns) pulsed laser irradiation. Ultraviolet–visible absorption spectrometry (UV-Vis), X-ray diffraction (XRD), and transmission electron microscopy (TEM) are used to characterize the obtained nanocrystal samples. The band gap energy of colloid is determined by analyzing the UV–Vis absorption spectra of the Ag2S NPs using the band theory of semiconductors. Z-scan technique is used to characterize the optical nonlinear properties of the Ag2S nanoparticles (NPs). Large enhancement of two photon absorption effect is observed with increase in concentration of the Ag2S nanoparticles using open Zscan measurements in the ns laser regime. The values of the nonlinear absorption coefficients are determined based on the local nonlinear responses including two photon absorption. The observed aperture dependence of the Ag2S NP limiting performance indicates that the nonlinear scattering plays an important role in the limiting action of the sample. The concentration dependence of the optical liming is also investigated. Our results demonstrate that the optical limiting threshold decreases with increasing the silver sulfide NPs in DMSO.

Keywords: Nanoscale materials, Silver sulfide nanoparticles, Nonlinear absorption, Nonlinear scattering, Optical limiting.

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Authors: A. Badoud, M. Khemliche, S. Latreche

Abstract:

The main objective developed in this paper is to find a graphic technique for modeling, simulation and diagnosis of the industrial systems. This importance is much apparent when it is about a complex system such as the nuclear reactor with pressurized water of several form with various several non-linearity and time scales. In this case the analytical approach is heavy and does not give a fast idea on the evolution of the system. The tool Bond Graph enabled us to transform the analytical model into graphic model and the software of simulation SYMBOLS 2000 specific to the Bond Graphs made it possible to validate and have the results given by the technical specifications. We introduce the analysis of the problem involved in the faults localization and identification in the complex industrial processes. We propose a method of fault detection applied to the diagnosis and to determine the gravity of a detected fault. We show the possibilities of application of the new diagnosis approaches to the complex system control. The industrial systems became increasingly complex with the faults diagnosis procedures in the physical systems prove to become very complex as soon as the systems considered are not elementary any more. Indeed, in front of this complexity, we chose to make recourse to Fault Detection and Isolation method (FDI) by the analysis of the problem of its control and to conceive a reliable system of diagnosis making it possible to apprehend the complex dynamic systems spatially distributed applied to the standard pressurized water nuclear reactor.

Keywords: Bond Graph, Modeling, Simulation, Monitoring, Analytical Redundancy Relations, Pressurized Water Reactor, Directed Graph.

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Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

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In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

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Authors: Wen-Chi Liu

Abstract:

This study applies a simple and powerful nonlinear unit root test to test the validity of long-run purchasing power parity (PPP)  in a sample of 10 East-Asian countries (i.e., China, Hong Kong,  Indonesia, Japan, Korea, Malaysia, Philippines, Singapore, Taiwan  and Thailand) over the period of March 1985 to September 2008. The empirical results indicate that PPP holds true for half of these 10  East-Asian countries under study, and the adjustment toward PPP is found to be nonlinear and in an asymmetric way. 

 

Keywords: Purchasing Power Parity, East-Asian Countries, Nonlinear Unit Root Test, Asymmetry.

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Authors: M. Elsisi, M. Soliman, M. A. S. Aboelela, W. Mansour

Abstract:

This paper considers the design of Dual Proportional- Integral (DPI) Load Frequency Control (LFC), using gravitational search algorithm (GSA). The design is carried out for nonlinear hydrothermal power system where generation rate constraint (GRC) and governor dead band are considered. Furthermore, time delays imposed by governor-turbine, thermodynamic process, and communication channels are investigated. GSA is utilized to search for optimal controller parameters by minimizing a time-domain based objective function. GSA-based DPI has been compared to Ziegler- Nichols based PI, and Genetic Algorithm (GA) based PI controllers in order to demonstrate the superior efficiency of the proposed design. Simulation results are carried for a wide range of operating conditions and system parameters variations.

Keywords: Gravitational Search Algorithm (GSA), Load Frequency Control (LFC), Dual Proportional-Integral (DPI) controller.

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Authors: A. Ghaffari, A. S. Mostafavi

Abstract:

Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, mitosis and cell division. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks that control the activities of cyclin-dependent kinases (CDK). The network can be modeled by a set of nonlinear differential equations and its behavior predicted by numerical simulation. In this paper, an innovative approach has been proposed that uses genetic algorithms to mine a set of behavior data output by a biological system in order to determine the kinetic parameters of the system. In our approach, the machine learning method is integrated with the framework of existent biological information in a wiring diagram so that its findings are expressed in a form of system dynamic behavior. By numerical simulations it has been illustrated that the model is consistent with experiments and successfully shown that such application of genetic algorithms will highly improve the performance of mathematical model of the cell division cycle to simulate such a complicated bio-system.

Keywords: Cell cycle, Cyclin-dependent kinase, Fission yeast, Genetic algorithms, Mathematical modeling, Wiring diagram

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Authors: M. H. Moradi, S. M. Moosavi, A. R. Reisi

Abstract:

The main objective of this paper is to investigate the enhancement of power system stability via coordinated tuning of Power System Stabilizers (PSSs) in a multi-machine power system. The design problem of the proposed controllers is formulated as an optimization problem. Chaotic catfish particle swarm optimization (C-Catfish PSO) algorithm is used to minimize the ITAE objective function. The proposed algorithm is evaluated on a two-area, 4- machines system. The robustness of the proposed algorithm is verified on this system under different operating conditions and applying a three-phase fault. The nonlinear time-domain simulation results and some performance indices show the effectiveness of the proposed controller in damping power system oscillations and this novel optimization algorithm is compared with particle swarm optimization (PSO).

Keywords: Power system stabilizer, C-Catfish PSO, ITAE objective function, Power system control, Multi-machine power system

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Authors: Magdi M. Nabi, Ding-Li Yu

Abstract:

Control of a semi-batch polymerization reactor using an adaptive radial basis function (RBF) neural network method is investigated in this paper. A neural network inverse model is used to estimate the valve position of the reactor; this method can identify the controlled system with the RBF neural network identifier. The weights of the adaptive PID controller are timely adjusted based on the identification of the plant and self-learning capability of RBFNN. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance and the nonlinear system is achieved.

Keywords: Chylla-Haase polymerization reactor, RBF neural networks, feed-forward and feedback control.

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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Authors: Panagiotis H. Tsarouhas

Abstract:

the reliability analysis of the medical equipments can help to increase the availability and the efficiency of the systems. In this manuscript we present a simple method of decomposition that could be easily applied on the complex medical systems. Using this method we can easily calculate the effect of the subsystems or components on the reliability of the overall system. Furthermore, to investigate the effect of subsystems or components on system performance, we perform a numerical study varying every time the worst reliability of subsystem or component with another which has higher reliability. It can also be useful to engineers and designers of medical equipment, who wishes to optimize the complex systems.

Keywords: Reliability, Availability, Series-parallel System, medical equipment.

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Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

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This paper presents a 4-DOF nonlinear model of a cracked de Laval rotor-stator system derived based on Energy Principles. The model has been used to simulate coupled torsionallateral response of the faulty system with multiple parametric excitations; rotor-stator-rub, a breathing transverse crack, eccentric mass and an axial force. Nonlinearity of a “breathing” crack is incorporated in the model using a simple hinge mechanism suitable for a shallow crack. Response of the system while passing via its critical speed with intermittent rotor-stator rub is analyzed. Effects of eccentricity with phase and acceleration are investigated. Features of crack, rub and eccentricity in vibration response are explored for condition monitoring. The presence of a crack and rub are observable in the power spectrum despite excitations by an axial force and rotor unbalance. Obtained results are consistent with existing literature and could be adopted into rotor condition monitoring strategies.

Keywords: Axial force, Crack, Nonlinear, Rotor-Stator, Rub.

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Authors: D.N. Zheng, J.X. Wang, Y.N. Zhao, Z.H. Yang

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The Linear discriminant analysis (LDA) can be generalized into a nonlinear form - kernel LDA (KLDA) expediently by using the kernel functions. But KLDA is often referred to a general eigenvalue problem in singular case. To avoid this complication, this paper proposes an iterative algorithm for the two-class KLDA. The proposed KLDA is used as a nonlinear discriminant classifier, and the experiments show that it has a comparable performance with SVM.

Keywords: Linear discriminant analysis (LDA), kernel LDA (KLDA), conjugate gradient algorithm, nonlinear discriminant classifier.

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Authors: Rabia Korkmaz Tan, Şebnem Bora

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The major problem encountered when modeling complex systems with agent-based modeling and simulation techniques is the existence of large parameter spaces. A complex system model cannot be expected to reflect the whole of the real system, but by specifying the most appropriate parameters, the actual system can be represented by the model under certain conditions. When the studies conducted in recent years were reviewed, it has been observed that there are few studies for parameter tuning problem in agent based simulations, and these studies have focused on tuning parameters of a single model. In this study, an approach of parameter tuning is proposed by using metaheuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Artificial Bee Colonies (ABC), Firefly (FA) algorithms. With this hybrid structured study, the parameter tuning problems of the models in the different fields were solved. The new approach offered was tested in two different models, and its achievements in different problems were compared. The simulations and the results reveal that this proposed study is better than the existing parameter tuning studies.

Keywords: Parameter tuning, agent based modeling and simulation, metaheuristic algorithms, complex systems.

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Through the emergence of modern architecture, an aggressive desire for new design theories appeared through the works of architects and critics. The discourse of complexity and volumetric composition happened to be an important and controversial issue in the discipline of architecture which was discussed through a general point of view in Robert Venturi and Denise Scott Brown's book “Complexity and contradiction in architecture” in 1966, this paper attempts to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. Accordingly, we identify chaotic architecture as the correlation between chaos theory and the discipline of architecture, and as an independent nonlinear design theory with specific characteristics and properties.

Keywords: Architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology.

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Authors: Abdullah M. Alodhaiani, Yasir A. Alturki, Mohamed A. Elkady

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Complex power flow distribution factors, which relate line complex power flows to the bus injected complex powers, have been widely used in various power system planning and analysis studies. In particular, AC distribution factors have been used extensively in the recent power and energy pricing studies in free electricity market field. As was demonstrated in the existing literature, many of the electricity market related costing studies rely on the use of the distribution factors. These known distribution factors, whether the injection shift factors (ISF’s) or power transfer distribution factors (PTDF’s), are linear approximations of the first order sensitivities of the active power flows with respect to various variables. This paper presents a novel model for evaluating the universal distribution factors (UDF’s), which are appropriate for an extensive range of power systems analysis and free electricity market studies. These distribution factors are used for the calculations of lines complex power flows and its independent of bus power injections, they are compact matrix-form expressions with total flexibility in determining the position on the line at which line flows are measured. The proposed approach was tested on IEEE 9-Bus system. Numerical results demonstrate that the proposed approach is very accurate compared with exact method.

Keywords: Distribution Factors, Power System, Sensitivity Factors, Electricity Market.

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Authors: Yahya Naderi, Tohid Rahimi, Babak Yousefi, Seyed Hossein Hosseini

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Today’s modern interconnected power system is highly complex in nature. In this, one of the most important requirements during the operation of the electric power system is the reliability and security. Power and frequency oscillation damping mechanism improve the reliability. Because of power system stabilizer (PSS) low speed response against of major fault such as three phase short circuit, FACTs devise that can control the network condition in very fast time, are becoming popular. But FACTs capability can be seen in a major fault present when nonlinear models of FACTs devise and power system equipment are applied. To realize this aim, the model of multi-machine power system with FACTs controller is developed in MATLAB/SIMULINK using Sim Power System (SPS) blockiest. Among the FACTs device, Static synchronous series compensator (SSSC) due to high speed changes its reactance characteristic inductive to capacitive, is effective power flow controller. Tuning process of controller parameter can be performed using different method. But Genetic Algorithm (GA) ability tends to use it in controller parameter tuning process. In this paper firstly POD controller is used to power oscillation damping. But in this station, frequency oscillation dos not has proper damping situation. So FOD controller that is tuned using GA is using that cause to damp out frequency oscillation properly and power oscillation damping has suitable situation.

Keywords: Power oscillation damping (POD), frequency oscillation damping (FOD), Static synchronous series compensator (SSSC), Genetic Algorithm (GA).

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Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

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In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

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Authors: Xu Tao, Yilun Xu, Dingwei Xiang, Yaofei Sun

Abstract:

The practice of urban planning and construction based on the concept of the “low carbon eco-city” has been universally accepted by the academic community in response to urban issues such as population, resources, environment, and social development. Based on this, the current article first analyzes the concepts of low carbon eco-city, then builds a complex adaptive system (CAS) theory based on Chinese traditional philosophical thinking, and analyzes the adaptive relationship between material and non-material elements. A three-dimensional evaluation model of natural ecology, economic low carbon, and social harmony was constructed. Finally, the construction of a low carbon eco-city index system in Hexi Newtown of Nanjing was used as an example to verify the effectiveness of the research results; this paradigm provides a new way to achieve a low carbon eco-city system.

Keywords: Complex adaptive system, low carbon ecology, index system, model.

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