Search results for: Kejun%20Zhuang
14 Hopf Bifurcation for a New Chaotic System
Authors: Kejun Zhuang
Abstract:
In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.
Keywords: Chaotic system, Hopf bifurcation, normal form theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 140613 Stability and Bifurcation Analysis in a Model of Hes1 Selfregulation with Time Delay
Authors: Kejun Zhuang, Hailong Zhu
Abstract:
The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem.Keywords: Hes1, Hopf bifurcation, time delay, transcriptional repression loop
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 134212 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, ratio–dependent, coincidence degree, periodic solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 146111 Periodic Solutions for a Delayed Population Model on Time Scales
Authors: Kejun Zhuang, Zhaohui Wen
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 130910 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: Predator-prey system, Stage structure, Hopf bifurcation, Periodic solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12899 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: Physiological control system, global Hopf bifurcation, periodic solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15118 Global Existence of Periodic Solutions in a Delayed Tri–neuron Network
Authors: Kejun Zhuang, Zhaohui Wen
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In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson-s criterion for high– dimensional ordinary differential equations and global Hopf bifurcation theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established.Keywords: Delay, global Hopf bifurcation, neural network, periodicsolutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14367 Dynamics and Feedback Control for a New Hyperchaotic System
Authors: Kejun Zhuang, Hailong Zhu
Abstract:
In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.Keywords: Feedback control, Hopf bifurcation, hyperchaotic system, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17036 Dynamical Behaviors in a Discrete Predator-prey Model with a Prey Refuge
Authors: Kejun Zhuang, Zhaohui Wen
Abstract:
By incorporating a prey refuge, this paper proposes new discrete Leslie–Gower predator–prey systems with and without Allee effect. The existence of fixed points are established and the stability of fixed points are discussed by analyzing the modulus of characteristic roots.
Keywords: Leslie-Gower, predator–prey model, prey refuge, allee effect.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15215 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, food chain model, coincidence degree, periodic solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16654 Periodicity for a Semi–Ratio–Dependent Predator–Prey System with Delays on Time Scales
Authors: Kejun Zhuang
Abstract:
In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.
Keywords: Semi–ratio–dependent, predator–prey system, coincidence degree, time scales.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12463 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, coincidence degree, food chain model, Crowley–Martin functional response.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18692 Periodic Solutions for a Food Chain System with Monod–Haldane Functional Response on Time Scales
Authors: Kejun Zhuang, Hailong Zhu
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 84201 A Contractor Iteration Method Using Eigenpairs for Positive Solutions of Nonlinear Elliptic Equation
Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang
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By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.
Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1330