Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 10

Periodic solutions Related Publications

10 Exponential Stability of Periodic Solutions in Inertial Neural Networks with Unbounded Delay

Authors: Yunquan Ke, Chunfang Miao

Abstract:

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: lyapunov function, exponential stability, Periodic solutions, Inertial neural networks, unbounded delay, fixed-point theorem

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1271
9 Existence and Global Exponential Stability of Periodic Solutions of Cellular Neural Networks with Distributed Delays and Impulses on Time Scales

Authors: Daiming Wang

Abstract:

In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.

Keywords: Periodic solutions, coincidence degree, Global exponential stability, M-matrix

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1130
8 Periodic Solutions of Recurrent Neural Networks with Distributed Delays and Impulses on Time Scales

Authors: Yaping Ren, Yongkun Li

Abstract:

In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.

Keywords: time scales, Recurrent Neural Networks, Periodic solutions, Global exponential stability, impulses, distributed delays

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1263
7 Dynamics of a Discrete Three Species Food Chain System

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

The main purpose of this paper is to investigate a discrete time three–species food chain system with ratio dependence. By employing coincidence degree theory and analysis techniques, sufficient conditions for existence of periodic solutions are established.

Keywords: Food Chain, Periodic solutions, coincidence degree, ratio–dependent

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1190
6 Bifurcation Analysis for a Physiological Control System with Delay

Authors: Kejun Zhuang

Abstract:

In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis.

Keywords: Periodic solutions, Global Hopf bifurcation, Physiological control system

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1298
5 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: time scales, Periodic solutions, coincidence degree, continuation theorem

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1035
4 Hopf Bifurcation Analysis for a Delayed Predator–prey System with Stage Structure

Authors: Kejun Zhuang

Abstract:

In this paper, a delayed predator–prey system with stage structure is investigated. Sufficient conditions for the system to have multiple periodic solutions are obtained when the delay is sufficiently large by applying Bendixson-s criterion. Further, some numerical examples are given.

Keywords: Hopf Bifurcation, Predator-prey system, Stage structure, Periodic solutions

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1042
3 Existence of Periodic Solutions in a Food Chain Model with Holling–type II Functional Response

Authors: Zhaohui Wen

Abstract:

In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin-s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: time scales, Periodic solutions, food chain model, coincidence degree

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1401
2 Analysis for a Food Chain Model with Crowley–Martin Functional Response and Time Delay

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper is concerned with a nonautonomous three species food chain model with Crowley–Martin type functional response and time delay. Using the Mawhin-s continuation theorem in theory of degree, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Periodic solutions, food chain model, coincidence degree, Crowley–Martin functional response

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1583
1 Periodicity for a Food Chain Model with Functional Responses on Time Scales

Authors: Kejun Zhuang

Abstract:

With the help of coincidence degree theory, sufficient conditions for existence of periodic solutions for a food chain model with functional responses on time scales are established.

Keywords: time scales, Periodic solutions, food chain model, coincidence degree

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1418