Search results for: Lyapunov exponents

Authors: Sarita Kumari, Ranjit Kumar Upadhyay

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This paper deals with plankton-fish dynamics where the fish population is growing logistically and nonlinearly harvested. The interaction between phytoplankton and zooplankton population is considered to be Crowley-Martin type functional response. It has been assumed that phytoplankton grows logistically and is affected by a space-dependent growth rate. Conditions for the existence of a positive equilibrium point and their stability analysis (both local and global) have been discussed for the non-spatial system. We have discussed maximum sustainable yields as well as optimal harvesting policy for maximizing the economic gain. The stability and existence of Hopf –bifurcation analysis have been discussed for the spatial system. Different conditions for turning pattern formation have been established through diffusion-driven instability analysis. Numerical simulations have been carried out for both non-spatial and spatial models. Phase plane analysis, the largest Lyapunov exponent, and bifurcation theory are used to numerically analyzed the non-spatial system. Our study shows that spatial heterogeneity, the mortality rate of phytoplankton, and constant harvesting of the fish population each play an important role in the dynamical behavior of the marine system.

Keywords: optimal harvesting, pattern formation, spatial heterogeneity, Crowley-Martin functional response

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In this paper, a robust fault-tolerant predictive control (FTPC) strategy is proposed for systems with linear parameter varying (LPV) models and input constraints subject to sensor faults. Generally, virtual observers are used for improving the observation precision and reduce the impacts of sensor faults and uncertainties in the system. However, this type of observer lacks certain system measurements which substantially reduce its accuracy. To deal with this issue, a real observer is then designed based on the virtual observer, and consequently a real observer-based robust predictive control is designed for polytopic LPV systems. Moreover, the proposed observer can entirely assure that all system states and sensor faults are estimated. As a result, and based on both observers, a robust fault-tolerant predictive control is then established via the Lyapunov method where sufficient conditions are proposed, for stability analysis and control purposes, in linear matrix inequalities (LMIs) form. Finally, simulation results are given to show the effectiveness of the proposed approach.

Keywords: linear parameter varying systems, fault-tolerant predictive control, observer-based control, sensor faults, input constraints, linear matrix inequalities

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Authors: Adam Ahmed Hosney

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The existence of a culture of corruption within an institution, such as the police, could be a sign of failure from various angles. There is a general perception among Ghanaians that the most corrupt institution is the police service. The purpose of this study is to formulate and analyze a nonlinear mathematical model to investigate corruption as an epidemic within the Ghana police service, this study revealed the basic reproduction number for corruption extinction and corruption survival. The threshold conditions for all kinds of equilibrium points are obtained using linearization methods and Lyapunov functional methods, and they demonstrate local asymptotic stability for both corrupt endemic and corrupt free equilibrium states. The model was analyzed qualitatively, and the solution was derived. The model appears to be positively invariant and attractive. Therefore, the region exhibits positive invariance. Thus, it is adequate to think about the dynamics of the model. For the purpose of illustrating the solution, the graphic result was presented and discussed. Results show that corruption will die out within the police service if the government shows no tolerance for those involved in corrupt practices. Study findings indicate that leaders should be trustworthy, demonstrate a complete and viable commitment to addressing corruption, and make it a priority to provide mass education to all citizens as well as using religious leaders to fight corruption since most Ghanaians are religious and trust their leaders.

Keywords: mathematical model, differential equation, dynamical system, simulation

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Authors: Alireza Gholami, Amir H. D. Markazi

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In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.

Keywords: adaptive algorithm, fuzzy systems, membership functions, observer

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Authors: Mrinalini Ranjan, Sudheesh Chethil

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Epilepsy is a common neurological disorder characterised by the recurrence of seizures. Electroencephalogram (EEG) signals are complex biomedical signals which exhibit nonlinear and nonstationary behavior. We use two methods 1) Detrended Fluctuation Analysis (DFA) and 2) Recurrence Plots (RP) to capture this complex behavior of EEG signals. DFA considers fluctuation from local linear trends. Scale invariance of these signals is well captured in the multifractal characterisation using detrended fluctuation analysis (DFA). Analysis of long-range correlations is vital for understanding the dynamics of EEG signals. Correlation properties in the EEG signal are quantified by the calculation of a scaling exponent. We report the existence of two scaling behaviours in the epileptic EEG signals which quantify short and long-range correlations. To illustrate this, we perform DFA on extant ictal (seizure) and interictal (seizure free) datasets of different patients in different channels. We compute the short term and long scaling exponents and report a decrease in short range scaling exponent during seizure as compared to pre-seizure and a subsequent increase during post-seizure period, while the long-term scaling exponent shows an increase during seizure activity. Our calculation of long-term scaling exponent yields a value between 0.5 and 1, thus pointing to power law behaviour of long-range temporal correlations (LRTC). We perform this analysis for multiple channels and report similar behaviour. We find an increase in the long-term scaling exponent during seizure in all channels, which we attribute to an increase in persistent LRTC during seizure. The magnitude of the scaling exponent and its distribution in different channels can help in better identification of areas in brain most affected during seizure activity. The nature of epileptic seizures varies from patient-to-patient. To illustrate this, we report an increase in long-term scaling exponent for some patients which is also complemented by the recurrence plots (RP). RP is a graph that shows the time index of recurrence of a dynamical state. We perform Recurrence Quantitative analysis (RQA) and calculate RQA parameters like diagonal length, entropy, recurrence, determinism, etc. for ictal and interictal datasets. We find that the RQA parameters increase during seizure activity, indicating a transition. We observe that RQA parameters are higher during seizure period as compared to post seizure values, whereas for some patients post seizure values exceeded those during seizure. We attribute this to varying nature of seizure in different patients indicating a different route or mechanism during the transition. Our results can help in better understanding of the characterisation of epileptic EEG signals from a nonlinear analysis.

Keywords: detrended fluctuation, epilepsy, long range correlations, recurrence plots

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Authors: Paulo Da Silva Quadros

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This work aims to point out comparative parameters between the artistic production of two exponents of the contemporary popular culture scene: Caetano Veloso (Brazil) and David Bowie (England). Both Caetano Veloso and David Bowie were pioneers in establishing an aesthetic game between various artistic expressions at the service of the music-visual scene, that is, the conceptual interconnections between several forms of aesthetic processes, such as fine arts, theatre, cinema, poetry, and literature. There are also correlations in their expressive attitudes of art, especially regarding the dialogue between the fields of art and politics (concern with respect to human rights, human dignity, racial issues, tolerance, gender issues, and sexuality, among others); the constant tension and cunning game between market, free expression and critical sense; the sophisticated, playful mechanisms of metalanguage and aesthetic metacritique. Fact is that both of them almost came to cooperate with each other in the 1970s when Caetano was in exile in England, and when both had at the same time the same music producer, who tried to bring them closer, noticing similar aesthetic qualities in both artistic works, which was later glimpsed by some music critics. Among many of the most influential issues in Caetano's and Bowie's game of artistic-aesthetic expression are, for example, the ideas advocated by the sensation of strangeness (Albert Camus), art as transcendence (Friedrich Nietzsche), the deconstruction and reconstruction of auratic reconfiguration of artistic signs (Walter Benjamin and Andy Warhol). For deepen more theoretical issues, the following authors will be used as supportive interpretative references: Hans-Georg Gadamer, Immanuel Kant, Friedrich Schiller, Johan Huizinga. In addition to the aesthetic meanings of Ars Ludens characteristics of the two artists, the following supporting references will be also added: the question of technique (Martin Heidegger), the logic of sense (Gilles Deleuze), art as an event and the sense of the gesture of art ( Maria Teresa Cruz), the society of spectacle (Guy Debord), Verarbeitung and Durcharbeitung (Sigmund Freud), the poetics of interpretation and the sign of relation (Cremilda Medina). The purpose of such interpretative references is to seek to understand, from a cultural reading perspective (cultural semiology), some significant elements in the dynamics of aesthetic and media interconnections of both artists, which made them as some of the most influential interlocutors in contemporary music aesthetic thought, as a playful vivid experience of life and art.

Keywords: Caetano Veloso, David Bowie, music aesthetics, symbolic playfulness, cultural reading

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Authors: Shabadini Sampath, Jinglang Feng

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With huge kinetic energy, space debris poses a major threat to astronauts’ space activities and spacecraft in orbit if a collision happens. The active removal of space debris is required in order to avoid frequent collisions that would occur. In addition, the amount of space debris will increase uncontrollably, posing a threat to the safety of the entire space system. But the safe and reliable removal of large-scale space debris has been a huge challenge to date. While capturing and deorbiting space debris, the space manipulator has to achieve high control precision. However, due to uncertainties and unknown disturbances, there is difficulty in coordinating the control of the space manipulator. To address this challenge, this paper focuses on developing a robust and intelligent control algorithm that controls joint movement and restricts it on the sliding manifold by reducing uncertainties. A neural network adaptive sliding mode controller (NNASMC) is applied with the objective of finding the control law such that the joint motions of the space manipulator follow the given trajectory. A computed torque control (CTC) is an effective motion control strategy that is used in this paper for computing space manipulator arm torque to generate the required motion. Based on the Lyapunov stability theorem, the proposed intelligent controller NNASMC and CTC guarantees the robustness and global asymptotic stability of the closed-loop control system. Finally, the controllers used in the paper are modeled and simulated using MATLAB Simulink. The results are presented to prove the effectiveness of the proposed controller approach.

Keywords: GNC, active removal of space debris, AI controllers, MatLabSimulink

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Authors: Jia Li, Huacong Li, Xiaobao Han

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Due to the more variable geometry parameters of VCE (variable cycle aircraft engine), presents an adaptive controller method based on the full-state linear model of VCE and has simulated to solve the multivariate controller design problem of the whole flight envelops. First, analyzes the static and dynamic performances of bypass ratio and other state parameters caused by variable geometric components, and develops nonlinear component model of VCE. Then based on the component model, through small deviation linearization of main fuel (Wf), the area of tail nozzle throat (A8) and the angle of rear bypass ejector (A163), setting up multiple linear model which variable geometric parameters can be inputs. Second, designs the adaptive controllers for VCE linear models of different nominal points. Among them, considering of modeling uncertainties and external disturbances, derives the adaptive law by lyapunov function. The simulation results showed that, the adaptive controller method based on full-state linear model used the angle of rear bypass ejector as input and effectively solved the multivariate control problems of VCE. The performance of all nominal points could track the desired closed-loop reference instructions. The adjust time was less than 1.2s, and the system overshoot was less than 1%, at the same time, the errors of steady states were less than 0.5% and the dynamic tracking errors were less than 1%. In addition, the designed controller could effectively suppress interference and reached the desired commands with different external random noise signals.

Keywords: variable cycle engine (VCE), full-state linear model, adaptive control, by-pass ratio

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Authors: Shruti Malviya, Chris Bowler

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Environmental processes acting at multiple spatial scales control marine diatom community structure. However, the contribution of local factors (e.g., temperature, salinity, etc.) in these highly complex systems is poorly understood. We, therefore, investigated the diatom community organization as a function of environmental predictors and determined the relative contribution of various environmental factors on the structure of marine diatoms assemblages in the world’s ocean. The dataset for this study was derived from the Tara Oceans expedition, constituting 46 sampling stations from diverse oceanic provinces. The V9 hypervariable region of 18s rDNA was organized into assemblages based on their distributional co-occurrence. Using Ward’s hierarchical clustering, nine clusters were defined. The number of ribotypes and reads varied within each cluster-three clusters (II, VIII and IX) contained only a few reads whereas two of them (I and IV) were highly abundant. Of the nine clusters, seven can be divided into two categories defined by a positive correlation with phosphate and nitrate and a negative correlation with longitude and, the other by a negative correlation with salinity, temperature, latitude and positive correlation with Lyapunov exponent. All the clusters were found to be remarkably dominant in South Pacific Ocean and can be placed into three classes, namely Southern Ocean-South Pacific Ocean clusters (I, II, V, VIII, IX), South Pacific Ocean clusters (IV and VII), and cosmopolitan clusters (III and VI). Our findings showed that co-occurring ribotypes can be significantly associated into recognizable clusters which exhibit a distinct response to environmental variables. This study, thus, demonstrated distinct behavior of each recognized assemblage displaying a taxonomic and environmental signature.

Keywords: assemblage, diatoms, hierarchical clustering, Tara Oceans

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Authors: Smita Lahkar

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Sattriya, the youngest of the eight principal Classical Indian dance traditions, has undergone too many changes and modifications to arrive at its present stage of performing art form extracting itself from age-old religious confinement. Although some of the other traditions have been revived in the recent past, Sattriya has a living tradition since its inception in the 15th century by Srimanta Sankardeva, the great Vaishnavite saint, poet, playwright, lyricist, painter, singer and dancer of Assam, a primary north-eastern state of India. This living dance tradition from the Sattras, the Vaishnavite monasteries, has been practiced for over five hundred years by celibate male monks, as a powerful medium for propagating the Vaishnava religious faith. Sankardeva realised the potential of the vocalised word integrated with the visual image as a powerful medium of expression and communication. So he used this principal medium for propagating his newly found message of devotion among the people of his time. Earlier, Sattriya was performed by male monks alone in monasteries (Sattras) as a part of daily rituals. The females were not even allowed to learn this art form. But, in present time, Sattriya has come out from the Sattras to proscenium stage, performed mostly by female as well as few male dancers also. The technique of performing movements, costumes, ornaments, music and style of performance too have experienced too many changes and modifications. For example, earlier and even today in Sattra, the ‘Pataka’ hand gesture is depicted in conformity with the original context (religious) of creation of the dance form. But, today stage-performers prefer the instructions of the scripture ‘Srihastamuktavali’ and depict the ‘Pataka’ in a sophisticated manner affecting decontextualisation to a certain extent. This adds aesthetic beauty to the dance form as an art distancing it from its context of being a vehicle for propagating Vaishnava religion. The Sattriya dance today stands at the crossroads of past and future, tradition and modernity, devotion and display, spirituality and secularism. The traditional exponents trained under the tutelage of Sattra maestros and imbibing a devotionally inspired rigour of the religion, try to retain the traditional nuances; while the young artists being trained outside the monasteries are more interested in taking up the discipline purely from the perspective of ‘performing arts’ bereft of the philosophy of religion or its sacred associations. Hence, this paper will be an endeavor to establish the hypothesis that the Sattriya, whose origin was for propagating Vaishnava faith, has now entered the world of performing arts with highly aesthetical components. And as a transformed art form, Sattriya may be expected to carve a niche in world dance arena. This will be done with the help of historical evidences, observations from the recorded past and expert rendezvous.

Keywords: dance, performing art, religion, Sattriya

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Authors: Magdy Roman, Mostafa Shoeib, Mostafa Rostom

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Global vision, whether provided by overhead fixed cameras, on-board aerial vehicle cameras, or satellite images can always provide detailed information on the environment around mobile robots. In this paper, an intelligent vision-based method of path planning and obstacle avoidance for mobile robots is presented. The method integrates visual perception with a new proposed field-based path-planning method to overcome common path-planning problems such as local minima, unreachable destination and unnecessary lengthy paths around obstacles. The method proposes an exponential angle deviation field around each obstacle that affects the orientation of a close robot. As the robot directs toward, the goal point obstacles are classified into right and left groups, and a deviation angle is exponentially added or subtracted to the orientation of the robot. Exponential field parameters are chosen based on Lyapunov stability criterion to guarantee robot convergence to the destination. The proposed method uses obstacles' shape and location, extracted from global vision system, through a collision prediction mechanism to decide whether to activate or deactivate obstacles field. In addition, a search mechanism is developed in case of robot or goal point is trapped among obstacles to find suitable exit or entrance. The proposed algorithm is validated both in simulation and through experiments. The algorithm shows effectiveness in obstacles' avoidance and destination convergence, overcoming common path planning problems found in classical methods.

Keywords: path planning, collision avoidance, convergence, computer vision, mobile robots

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Authors: Kayode Oshinubi, Brice Kammegne, Jacques Demongeot

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The use of mathematical tools like Partial Differential Equations and Ordinary Differential Equations have become very important to predict the evolution of a viral disease in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China causing a severe and potentially fatal respiratory syndrome, i.e., COVID-19. Since then, it has become a pandemic declared by World Health Organization (WHO) on March 11, 2020 which has spread around the globe. A reaction-diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process in which different substances are transformed, and a diffusion process that causes a distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined using the Lyapunov function are considered and the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. Also, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We showed the spatial distribution of the model compartments when the basic reproduction rate $\mathcal{R}_0 < 1$ and $\mathcal{R}_0 > 1$ and sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations. We investigate the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. To the public health policymakers, we offered a better understanding of the COVID-19 management.

Keywords: COVID-19, SEIRV epidemic model, reaction-diffusion equation, basic reproduction number, vaccination, spatial distribution

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Authors: Mohd Sabri Minhat, Nurul Adilla Mohd Subha

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The PUSPATI TRIGA Reactor (RTP), Malaysia reached its first criticality on June 28, 1982, with power capacity 1MW thermal. The Feedback Control Algorithm (FCA) which is conventional Proportional-Integral (PI) controller, was used for present power control method to control fission process in RTP. It is important to ensure the core power always stable and follows load tracking within acceptable steady-state error and minimum settling time to reach steady-state power. At this time, the system could be considered not well-posed with power tracking performance. However, there is still potential to improve current performance by developing next generation of a novel design nuclear core power control. In this paper, the dual-mode predictions which are proposed in modelling Optimal Model Predictive Control (OMPC), is presented in a state-space model to control the core power. The model for core power control was based on mathematical models of the reactor core, OMPC, and control rods selection algorithm. The mathematical models of the reactor core were based on neutronic models, thermal hydraulic models, and reactivity models. The dual-mode prediction in OMPC for transient and terminal modes was based on the implementation of a Linear Quadratic Regulator (LQR) in designing the core power control. The combination of dual-mode prediction and Lyapunov which deal with summations in cost function over an infinite horizon is intended to eliminate some of the fundamental weaknesses related to MPC. This paper shows the behaviour of OMPC to deal with tracking, regulation problem, disturbance rejection and caters for parameter uncertainty. The comparison of both tracking and regulating performance is analysed between the conventional controller and OMPC by numerical simulations. In conclusion, the proposed OMPC has shown significant performance in load tracking and regulating core power for nuclear reactor with guarantee stabilising in the closed-loop.

Keywords: core power control, dual-mode prediction, load tracking, optimal model predictive control

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Authors: S. Behnia, S. Fathizadeh, A. Akhshani

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In the recent decades, DNA has increasingly interested in the potential technological applications that not directly related to the coding for functional proteins that is the expressed in form of genetic information. One of the most interesting applications of DNA is related to the construction of nanostructures of high complexity, design of functional nanostructures in nanoelectronical devices, nanosensors and nanocercuits. In this field, DNA is of fundamental interest to the development of DNA-based molecular technologies, as it possesses ideal structural and molecular recognition properties for use in self-assembling nanodevices with a definite molecular architecture. Also, the robust, one-dimensional flexible structure of DNA can be used to design electronic devices, serving as a wire, transistor switch, or rectifier depending on its electronic properties. In order to understand the mechanism of the charge transport along DNA sequences, numerous studies have been carried out. In this regard, conductivity properties of DNA molecule could be investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model. In SSH model, the non-diagonal matrix element dependence on intersite displacements is considered. In this approach, the coupling between the charge and lattice deformation is along the helix. This model is a tight-binding linear nanoscale chain established to describe conductivity phenomena in doped polyethylene. It is based on the assumption of a classical harmonic interaction between sites, which is linearly coupled to a tight-binding Hamiltonian. In this work, the Hamiltonian and corresponding motion equations are nonlinear and have high sensitivity to initial conditions. Then, we have tried to move toward the nonlinear dynamics and phase space analysis. Nonlinear dynamics and chaos theory, regardless of any approximation, could open new horizons to understand the conductivity mechanism in DNA. For a detailed study, we have tried to study the current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram.

Keywords: DNA conductivity, Landauer resistance, negative dierential resistance, Chaos theory, mean Lyapunov exponent

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Authors: Yamina Boughari, Ruxandra Mihaela Botez, Florian Theel, Georges Ghazi

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Clearance of flight control laws of a civil aircraft is a long and expensive process in the Aerospace industry. Thousands of flight combinations in terms of speeds, altitudes, gross weights, centers of gravity and angles of attack have to be investigated, and proved to be safe. Nonetheless, in this method, a worst flight condition can be easily missed, and its missing would lead to a critical situation. Definitively, it would be impossible to analyze a model because of the infinite number of cases contained within its flight envelope, that might require more time, and therefore more design cost. Therefore, in industry, the technique of the flight envelope mesh is commonly used. For each point of the flight envelope, the simulation of the associated model ensures the satisfaction or not of specifications. In order to perform fast, comprehensive and effective analysis, other varying parameters models were developed by incorporating variations, or uncertainties in the nominal models, known as Linear Fractional Representation LFR models; these LFR models were able to describe the aircraft dynamics by taking into account uncertainties over the flight envelope. In this paper, the LFRs models are developed using the speeds and altitudes as varying parameters; The LFR models were built using several flying conditions expressed in terms of speeds and altitudes. The use of such a method has gained a great interest by the aeronautical companies that have seen a promising future in the modeling, and particularly in the design and certification of control laws. In this research paper, we will focus on the Cessna Citation X open loop stability analysis. The data are provided by a Research Aircraft Flight Simulator of Level D, that corresponds to the highest level flight dynamics certification; this simulator was developed by CAE Inc. and its development was based on the requirements of research at the LARCASE laboratory. The acquisition of these data was used to develop a linear model of the airplane in its longitudinal and lateral motions, and was further used to create the LFR’s models for 12 XCG /weights conditions, and thus the whole flight envelope using a friendly Graphical User Interface developed during this study. Then, the LFR’s models are analyzed using Interval Analysis method based upon Lyapunov function, and also the ‘stability and robustness analysis’ toolbox. The results were presented under the form of graphs, thus they have offered good readability, and were easily exploitable. The weakness of this method stays in a relatively long calculation, equal to about four hours for the entire flight envelope.

Keywords: flight control clearance, LFR, stability analysis, robustness analysis

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