Search results for: asymptotically periodic

Authors: Ziping Li, Yongkun Li

Abstract:

In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.

Keywords: Discrete cooperation model, almost periodic solution, feedback control, Lyapunov function.

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Authors: Changjin Xu, Yusen Wu

Abstract:

In this paper, a asymptotically periodic predator-prey model with Modified Leslie-Gower and Holling-Type II schemes is investigated. Some sufficient conditions for the uniformly strong persistence of the system are established. Our result is an important complementarity to the earlier results.

Keywords: Predator-prey model, uniformly strong persistence, asymptotically periodic, Holling-type II.

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Authors: Shunyi Li, Zhifang He, Xiangui Xue

Abstract:

An Ivlev-type predator-prey system and stage-structured for predator concerning impulsive control strategy is considered. The conditions for the locally asymptotically stable prey-eradication periodic solution is obtained, by using Floquet theorem and small amplitude perturbation skills——when the impulsive period is less than the critical value. Otherwise, the system is permanence. Numerical examples show that the system considered has more complicated dynamics, including high-order quasi-periodic and periodic oscillating, period-doubling and period-halving bifurcation, chaos and attractor crisis, etc. Finally, the biological implications of the results and the impulsive control strategy are discussed.

Keywords: Stage-structured predator-prey system, Impulsive, Permanence, Bifurcation, Chaos.

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Authors: Ru-Shuo Sheu, Han-Hsin Chou, Te-Shyang Tan

Abstract:

Considering a reservoir with periodic states and different cost functions with penalty, its release rules can be modeled as a periodic Markov decision process (PMDP). First, we prove that policy- iteration algorithm also works for the PMDP. Then, with policy- iteration algorithm, we obtain the optimal policies for a special aperiodic reservoir model with two cost functions under large penalty and give a discussion when the penalty is small.

Keywords: periodic Markov decision process, periodic state, policy-iteration algorithm.

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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Authors: Changjin Xu

Abstract:

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Antonio Mauricio F. L. Miranda de Sá

Abstract:

Partial coherence between two signals removing the contribution of a periodic, deterministic signal is proposed for evaluating the interrelationship in multivariate systems. The estimator expression was derived and shown to be independent of such periodic signal. Simulations were used for obtaining its critical value, which were found to be the same as those for Gaussian signals, as well as for evaluating the technique. An Illustration with eletroencephalografic (EEG) signals during photic stimulation is also provided. The application of the proposed technique in both simulation and real EEG data indicate that it seems to be very specific in removing the contribution of periodic sources. The estimate independence of the periodic signal may widen partial coherence application to signal analysis, since it could be used together with simple coherence to test for contamination in signals by a common, periodic noise source.

Keywords: Partial coherence, periodic input, spectral analysis, statistical signal processing.

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Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

Keywords: Coincidence degree, continuation theorem, periodic solutions, time scales

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Authors: Lili Wang, Meng Hu

Abstract:

In this paper, based on almost periodic functional hull theory and M-matrix theory, some sufficient conditions are established for the existence and uniqueness of positive almost periodic solution for a class of BAM neural networks with time-varying delays. An example is given to illustrate the main results.

Keywords: Delayed BAM neural networks, Hull theorem, Mmatrix, Almost periodic solution, Global exponential stability.

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Authors: Takashi Mitsuishi, Koji Saigusa

Abstract:

This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.

Keywords: Defuzzification, periodic membership function, polar coordinates transformation.

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Authors: Farouk Cherif

Abstract:

This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.

Keywords: Chaotic neural network, Hamiltonian systems, Pseudo almost periodic.

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Authors: Xiaoquan Ding, Jianmin Hao, Changwen Liu

Abstract:

This paper is devoted to a delayed periodic predatorprey system with non-monotonic numerical response on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones.

Keywords: Predator-prey system, periodic solution, time scale, delay, coincidence degree.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, we investigate dynamics of 2n almost periodic attractors for Cohen-Grossberg neural networks (CGNNs) with variable and distribute time delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CGNNs into 2n compact convex subsets. Then the existence of 2n almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder-s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2n almost periodic solutions and exponential attracting domains are also given correspondingly.

Keywords: CGNNs, almost periodic solution, invariant basins, attracting domains.

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Authors: Zhouhong Li, Jiming Yang

Abstract:

In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin-s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.

Keywords: Positive periodic solutions, Predator-prey-chain model, coincidence degree, harvesting term.

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Authors: Fengshuo Zhang, Zhouhong Li

Abstract:

In this paper, we obtain sufficient conditions for the existence of at least four positive almost periodic solutions to an impulsive delayed periodic plankton allelopathy system with multiple exploited (or harvesting) terms. This result is obtained through the use of Mawhins continuation theorem of coincidence degree theory along with some properties relating to inequalities.

Keywords: Almost periodic solutions, plankton allelopathy system, coincidence degree, impulse.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural networks, Lyapunov-Krasovskii, Time-varying delays, Linear matrix inequality.

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

Keywords: Asypmtotically quasi-nonexpansive mappings, Commonfixed point, Strong and weak convergence, Iteration process.

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Authors: Pan Wang, Yongkun Li

Abstract:

In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result.

Keywords: Periodic solution, predator-prey system, harvesting terms, continuation theorem.

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Authors: Zhouhong Li

Abstract:

In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.

Keywords: Almost periodic solution, Multi-delay, Logarithmic population model, Coincidence degree.

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Authors: Lili Wang, Meng Hu

Abstract:

In this paper, a class of recurrent neural networks (RNNs) with variable delays are studied on almost periodic time scales, some sufficient conditions are established for the existence and global exponential stability of the almost periodic solution. These results have important leading significance in designs and applications of RNNs. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.

Keywords: Recurrent neural network, Almost periodic solution, Global exponential stability, Time scale.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Ali Emad

Abstract:

Enhancement of the performance of a reverse osmosis (RO) unit through periodic control is studied. The periodic control manipulates the feed pressure and flow rate of the RO unit. To ensure the periodic behavior of the inputs, the manipulated variables (MV) are transformed into the form of sinusoidal functions. In this case, the amplitude and period of the sinusoidal functions become the surrogate MV and are thus regulated via nonlinear model predictive control algorithm. The simulation results indicated that the control system can generate cyclic inputs necessary to enhance the closedloop performance in the sense of increasing the permeate production and lowering the salt concentration. The proposed control system can attain its objective with arbitrary set point for the controlled outputs. Successful results were also obtained in the presence of modeling errors.

Keywords: Reverse osmosis, water desalination, periodic control, model predictive control.

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Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

Abstract:

In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

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Authors: Rana Khalid Naeem, Asif Mansoor

Abstract:

Periodicities in the environmetric time series can be idyllically assessed by utilizing periodic models. In this communication fugitive emission of gases from open sewer channel Lyari which follows periodic behaviour are approximated by employing periodic autoregressive model of order p. The orders of periodic model for each season are selected through the examination of periodic partial autocorrelation or information criteria. The parameters for the selected order of season are estimated individually for each emitted air toxin. Subsequently, adequacies of fitted models are established by examining the properties of the residual for each season. These models are beneficial for schemer and administrative bodies for the improvement of implemented policies to surmount future environmental problems.

Keywords: Exchange of Gases, Goodness of Fit, Open Sewer Channel, PAR(p) Models, Periodicities, Season Wise Models.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

Abstract:

In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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Authors: Ayşe Eldem, Fatih Başçiftçi

Abstract:

Visually impaired individuals cannot lead their lives as comfortable as others. Therefore, new applications are being developed every passing day in order to make their lives easier. In this study, an electronic and computer-aided audio device was developed with the aim of making the learning of the periodic table easier for the visually impaired. In this device, a board includes buttons for each element of the periodic table. After pressing a button, the visually impaired individual not only hears the name of the element but also feels with his/her hands where that specific element is located.

Keywords: Periodic Table, PIC16F877, Serial port, Visually Impaired Individual.

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Authors: Lili Wang

Abstract:

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and  effectiveness of the results.

Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Daiming Wang

Abstract:

In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.

Keywords: Neutral impulsive delay system, competitive system, coincidence degree, periodic solution, existence.

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Authors: Chenxi Yang, Zhouhong Li

Abstract:

This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.

Keywords: Permanence, Almost periodic solution, Epidemic model, Delay, Feedback control.

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