**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2598

# Search results for: Almost periodic solution

##### 2598 Almost Periodic Sequence Solutions of a Discrete Cooperation System with Feedback Controls

**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.

##### 2597 A Novel Approach to Positive Almost Periodic Solution of BAM Neural Networks with Time-Varying Delays

**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.

##### 2596 Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks

**Authors:**
Qianhong Zhang,
Lihui Yang,
Daixi Liao

**Abstract:**

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

##### 2595 Periodic Solutions for a Two-prey One-predator System on Time Scales

**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.

##### 2594 Almost Periodic Solution for an Impulsive Neural Networks with Distributed Delays

**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.

##### 2593 Existence and Exponential Stability of Almost Periodic Solution for Recurrent Neural Networks on Time Scales

**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.

##### 2592 Almost Periodic Solution for a Food-limited Population Model with Delay and Feedback Control

**Authors:**
Xiaoyan Dou,
Yongkun Li

**Abstract:**

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

**Keywords:**
Almost periodic solution,
food-limited population,
feedback control,
permanence.

##### 2591 Existence and Exponential Stability of Almost Periodic Solution for Cohen-Grossberg SICNNs with Impulses

**Abstract:**

In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.

**Keywords:**
Almost periodic solution,
exponential stability,
neural networks,
impulses.

##### 2590 Positive Almost Periodic Solutions for Neural Multi-Delay Logarithmic Population Model

**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.

##### 2589 Positive Periodic Solutions for a Neutral Impulsive Delay Competition System

**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.

##### 2588 Permanence and Almost Periodic Solutions to an Epidemic Model with Delay and Feedback Control

**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.

##### 2587 Application of He-s Amplitude Frequency Formulation for a Nonlinear Oscillator with Fractional Potential

**Abstract:**

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.

##### 2586 Pseudo-almost Periodic Solutions of a Class Delayed Chaotic Neural Networks

**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.

##### 2585 Multiple Periodic Solutions for a Delayed Predator-prey System on Time Scales

**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.

##### 2584 Existence of Periodic Solution for p-Laplacian Neutral Rayleigh Equation with Sign-variable Coefficient of Non Linear Term

**Authors:**
Aomar Anane,
Omar Chakrone,
Loubna Moutaouekkil

**Abstract:**

As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change signs in this paper, which are different from the corresponding ones of known literature.

**Keywords:**
periodic solution,
neutral Rayleigh equation,
variable
sign,
Deviating argument,
p-Laplacian,
Mawhin’s continuation.

##### 2583 Multiple Positive Periodic Solutions to a Predator-prey system with Harvesting Terms and Holling II Type Functional Response

**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.

##### 2582 2n Almost Periodic Attractors for Cohen-Grossberg Neural Networks with Variable and Distribute Delays

**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.

##### 2581 Equatorial Symmetry of Chaotic Solutions in Boussinesq Convection in a Rotating Spherical Shell

**Authors:**
Keiji Kimura,
Shin-ichi Takehiro,
Michio Yamada

**Abstract:**

**Keywords:**
thermal convection,
numerical simulation,
equatorial
symmetry,
quasi-periodic solution,
chaotic solution

##### 2580 Periodic Solutions in a Delayed Competitive System with the Effect of Toxic Substances on Time Scales

**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.

##### 2579 Periodic Solutions for a Third-order p-Laplacian Functional Differential Equation

**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.

##### 2578 Periodic Solutions for a Higher Order Nonlinear Neutral Functional Differential Equation

**Authors:**
Yanling Zhu

**Abstract:**

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

**Keywords:**
Neutral functional differential equation,
higher order,
periodic solution,
coincidence degree theory.

##### 2577 Robust Conversion of Chaos into an Arbitrary Periodic Motion

**Authors:**
Abolhassan Razminia,
Mohammad-Ali Sadrnia

**Abstract:**

One of the most attractive and important field of chaos theory is control of chaos. In this paper, we try to present a simple framework for chaotic motion control using the feedback linearization method. Using this approach, we derive a strategy, which can be easily applied to the other chaotic systems. This task presents two novel results: the desired periodic orbit need not be a solution of the original dynamics and the other is the robustness of response against parameter variations. The illustrated simulations show the ability of these. In addition, by a comparison between a conventional state feedback and our proposed method it is demonstrated that the introduced technique is more efficient.

**Keywords:**
chaos,
feedback linearization,
robust control,
periodic motion.

##### 2576 Periodic Solutions for a Food Chain System with Monod–Haldane Functional Response on Time Scales

**Authors:**
Kejun Zhuang,
Hailong Zhu

**Abstract:**

In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.

**Keywords:**
Food chain system,
periodic solution,
time scales,
coincidence degree.

##### 2575 Periodic Storage Control Problem

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

**Abstract:**

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

##### 2574 Anti-periodic Solutions for Cohen-Grossberg Shunting Inhibitory Neural Networks with Delays

**Authors:**
Yongkun Li,
Tianwei Zhang,
Shufa Bai

**Abstract:**

By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.

**Keywords:**
Anti-periodic solution,
coincidence degree,
global exponential stability,
Cohen-Grossberg shunting inhibitory cellular neural networks.

##### 2573 Evaluating Spectral Relationships between Signals by Removing the Contribution of a Common, Periodic Source A Partial Coherence-based Approach

**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.

##### 2572 Periodic Solutions for a Delayed Population Model on Time Scales

**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

##### 2571 Almost Periodicity in a Harvesting Lotka-Volterra Recurrent Neural Networks with Time-Varying Delays

**Authors:**
Yongzhi Liao

**Abstract:**

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.

**Keywords:**
positive almost periodic solution,
Lotka-Volterra,
neural
networks,
Banach fixed point theorem,
harvesting

##### 2570 Positive Periodic Solutions for a Predator-prey Model with Modified Leslie-Gower Holling-type II Schemes and a Deviating Argument

**Authors:**
Yanling Zhu,
Kai Wang

**Abstract:**

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

**Keywords:**
Predator-prey model,
Holling II type functional response,
positive periodic solution,
coincidence degree theorem.

##### 2569 Extension of the Client-Centric Approach under Small Buffer Space

**Authors:**
Hsiang-Fu Yu,
Yu-Chan Hsu,
Chun Fang,
Hao-Yun Yang

**Abstract:**

Periodic broadcast is a cost-effective solution for large-scale distribution of popular videos because this approach guarantees constant worst service latency, regardless of the number of video requests. An essential periodic broadcast method is the client-centric approach (CCA), which allows clients to use smaller receiving bandwidth to download broadcast data. An enhanced version, namely CCA++, was proposed to yield a shorter waiting time. This work further improves CCA++ in reducing client buffer requirements. The new scheme decreases the buffer requirements by as much as 52% when compared to CCA++. This study also provides an analytical evaluation to demonstrate the performance advantage, as compared with particular schemes.

**Keywords:**
Periodic broadcast,
client-centric approach,
buffer space,
multimedia communications.