Hopf Bifurcation and Stability Crossing Curve in a Planktonic Resource–Consumer System with Double Delays

2020 ◽  
Vol 30 (13) ◽  
pp. 2050190
Author(s):  
Zhichao Jiang ◽  
Yanfen Guo
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Parameter Plane ◽  
Dynamical Analysis ◽  
Existence Of Equilibrium ◽  
Two Delays ◽  
Simulation Results ◽  
Bifurcation And Stability ◽  
Theoretical Analyses

In this paper, a planktonic resource–consumer system with two delays is investigated and the coefficients depend on [Formula: see text] one of the two delays. Firstly, the property of solution and the existence of equilibrium are given. The dynamical analysis of the system including stability and Hopf bifurcation by using the delays as parameters is carried out. Both the single delay and two delays can cause the system to produce Hopf bifurcation and the stable switching phenomena may exist. Furthermore, using the crossing curve methods, we obtain the stable changes of equilibrium in two-delay parameter plane, which generalizes the results of the system that the coefficients do not depend on delay. Furthermore, the numerical simulation results show that the theoretical analyses are correct when the delays change.

scholarly journals Dynamical Analysis of a Computer Virus Model with Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-21 ◽  
Author(s):  
Juan Liu ◽  
Carlo Bianca ◽  
Luca Guerrini
Keyword(s):  
Hopf Bifurcation ◽  
Characteristic Root ◽  
Computer Virus ◽  
Dynamical Analysis ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Two Delays ◽  
Virus Model ◽  
Bifurcation And Stability

An SIQR computer virus model with two delays is investigated in the present paper. The linear stability conditions are obtained by using characteristic root method and the developed asymptotic analysis shows the onset of a Hopf bifurcation occurs when the delay parameter reaches a critical value. Moreover the direction of the Hopf bifurcation and stability of the bifurcating period solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical investigations are carried out to show the feasibility of the theoretical results.

scholarly journals Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Infection Model ◽  
Virus Propagation ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Two Delays ◽  
The Stability

This paper is devoted to the study of an SIRS computer virus propagation model with two delays and multistate antivirus measures. We demonstrate that the system loses its stability and a Hopf bifurcation occurs when the delay passes through the corresponding critical value by choosing the possible combination of the two delays as the bifurcation parameter. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to illustrate the obtained results.

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

scholarly journals Controlling Hyper Chaos with Feedback of Dynamical Variables

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4272-4277 ◽  
Author(s):  
Xiao-Shu Luo ◽  
Bing-Hong Wang
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Chaotic Attractors ◽  
Chaotic Circuit ◽  
Controlled System ◽  
Controlling Chaos ◽  
Simulation Results ◽  
System Variables ◽  
Proportional Feedback

We propose a method for controlling chaos and hyper-chaos by applying continuous proportional feedback to the system variables and their derivatives. The method has been applied successfully in six-order coupled Chua's hyper-chaotic circuit system. The theoretical analysis and numerical simulation results show that unstable fixed points embedded in hyper-chaotic attractors can be stabilized and Hopf bifurcation can be observed for the controlled system.

Stability and bifurcation analysis for a delayed viral infection model with full logistic proliferation

2020 ◽  
Vol 13 (05) ◽  
pp. 2050033
Author(s):  
Yan Geng ◽  
Jinhu Xu
Keyword(s):  
Hopf Bifurcation ◽  
Viral Infection ◽  
Time Delays ◽  
Infection Model ◽  
Lyapunov Functionals ◽  
Stability Switches ◽  
Two Delays ◽  
Infected Cells ◽  
Bifurcation And Stability ◽  
Viral Infection Model

In this paper, we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells. The global asymptotic stabilities of the equilibria are studied by constructing Lyapunov functionals. Moreover, we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation parameters. The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation. Finally, numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.

Hopf Bifurcation and Hidden Attractors of a Delay-Coupled Duffing Oscillator

2015 ◽  
Vol 25 (12) ◽  
pp. 1550162 ◽  
Author(s):  
Huitao Zhao ◽  
Yiping Lin ◽  
Yunxian Dai
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Stable Equilibrium ◽  
Duffing Oscillator ◽  
Sufficient Conditions ◽  
Hidden Attractors ◽  
Characteristic Roots ◽  
Delayed System ◽  
Simulation Results ◽  
Spatio Temporal

In this paper, a delay-coupled Duffing equation is studied. By the characteristic roots technique, sufficient conditions are obtained for Hopf bifurcation occurrence. And the spatio-temporal patterns of the bifurcating periodic solutions are also obtained, some examples are given to demonstrate the theoretical analysis. Especially, the obtained numerical simulation results show that there are hidden attractors in this delayed system, which can coexist with stable equilibrium or stable bifurcating orbits.

The R&D Research of Digital Content Platform Analysis Based on Numerical Simulation

2013 ◽  
Vol 756-759 ◽  
pp. 4716-4720
Author(s):  
Fu Jin Zhang ◽  
Jie Shang ◽  
Bin Wang
Keyword(s):  
Numerical Simulation ◽  
Nash Equilibrium ◽  
Network Size ◽  
Network Externality ◽  
Digital Content ◽  
High Tech ◽  
Existence Of Equilibrium ◽  
Technological Gap ◽  
Simulation Results ◽  
Research Show

This paper studies the related problems which belong to research of digital content platform by using numerical simulation. Results from the research show that: under effect of network externality, the digital content platform with high-tech stock could only expand successfully when the network size beyond critical capacity. But, when the technological gap is big enough, the critical capacity could be 0. Besides, we found the Nash equilibrium of R&D input is not necessary exist in the simulation without price, and the existence of equilibrium need special condition.

scholarly journals Dynamic Analysis and Degenerate Hopf Bifurcation-Based Feedback Control of a Conservative Chaotic System and Its Circuit Simulation

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Xiaojuan Zhang ◽  
Mingshu Chen ◽  
Yang Wang ◽  
Huaigu Tian ◽  
Zhen Wang
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Feedback Control ◽  
Chaotic System ◽  
Analog Circuit ◽  
Simulation Analysis ◽  
Circuit Simulation ◽  
State Feedback Control ◽  
Stable Domain ◽  
Simulation Results

A novel conservative chaotic system with no equilibrium is investigated in this study. Various dynamics such as the conservativeness, coexistence, symmetry, and invariance are presented. Furthermore, a partial-state feedback control scheme is proposed, and the stable domain of control parameters is analyzed based on the degenerate Hopf bifurcation. In order to verify the numerical simulation analysis, an analog circuit is designed. The simulation results show that the output of the analog circuit system can reproduce the numerical simulation results and verify the correctness of the theoretical analysis.

scholarly journals Analysis of the Stability and Hopf Bifurcation of Currency Supply Delay in an Opened Kaldorian Business Cycle Model

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Liming Zhao ◽  
Zhipei Zhao
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Business Cycle ◽  
Three Dimension ◽  
Cycle Model ◽  
Macroeconomic Policies ◽  
Existence Of Equilibrium ◽  
Business Cycle Model ◽  
The Stability ◽  
Theoretical Results

First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.

Avalanche Features in Silicon Schottky-FETs in Accordance with Numerical Simulation Results

2006 ◽  
Vol 65 (16) ◽  
pp. 1533-1546
Author(s):  
Yu. Ye. Gordienko ◽  
S. A. Zuev ◽  
V. V. Starostenko ◽  
V. Yu. Tereshchenko ◽  
A. A. Shadrin
Keyword(s):  
Numerical Simulation ◽  
Simulation Results
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