ECO-EPIDEMIOLOGICAL MODELS OF SALTON SEA WITH INFECTED PREY

2013 ◽  
Vol 21 (01) ◽  
pp. 1350003 ◽  
Author(s):  
Q. J. A. KHAN ◽  
E. BALAKRISHNAN ◽  
AZZA HAMOOD AL HARTHI
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Salton Sea ◽  
Bifurcation Parameter ◽  
Epidemiological Models ◽  
Analytical Results ◽  
Infected Prey

Two models for the interaction of susceptible and infected Tilapia population with Pelican population are studied. Here, we considered that Pelican interact with both susceptible and infected Tilapia in proportion to their abundance. Stability near nonzero equilibria is presented. In the second model, time delay is incorporated in the disease transmission term and Hopf bifurcation is analyzed by taking time delay as a bifurcation parameter. Numerical simulations are performed to support the analytical results.

Dynamics in a Van Der Pol Model with Delay

2012 ◽  
Vol 204-208 ◽  
pp. 4586-4589
Author(s):  
Chang Jin Xu ◽  
Pei Luan Li ◽  
Ling Yun Yao
Keyword(s):  
Asymptotic Behavior ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Bifurcation Parameter ◽  
Bifurcation Problem ◽  
Van Der Pol ◽  
Van Der Pol Model ◽  
The Stability

In this paper, the dynamics of a van der pol model with delay are considered. It is shown that the asymptotic behavior depends crucially on the time delay parameter. By regarded the delay as a bifurcation parameter, we are particularly interested in the study of the Hopf bifurcation problem. The length of delay which preserves the stability of the equilibrium is calculated. Some numerical simulations for justifying the analytical findings are included.

scholarly journals Stability and Hopf Bifurcation Analysis of a Fractional-Order Epidemic Model with Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhen Wang ◽  
Xinhe Wang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Bifurcation Parameter ◽  
Theoretical Results ◽  
Disease Free

A fractional-order epidemic model with time delay is considered. Firstly, stability of the disease-free equilibrium point and endemic equilibrium point is studied. Then, by choosing the time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical results.

scholarly journals A time-delay COVID-19 propagation model considering supply chain transmission and hierarchical quarantine rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fangfang Yang ◽  
Zizhen Zhang
Keyword(s):  
Supply Chain ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Local Stability ◽  
Propagation Model ◽  
Bifurcation Parameter ◽  
Two Delays ◽  
Chain Transmission ◽  
Theoretical Results

AbstractIn this manuscript, we investigate a novel Susceptible–Exposed–Infected–Quarantined–Recovered (SEIQR) COVID-19 propagation model with two delays, and we also consider supply chain transmission and hierarchical quarantine rate in this model. Firstly, we analyze the existence of an equilibrium, including a virus-free equilibrium and a virus-existence equilibrium. Then local stability and the occurrence of Hopf bifurcation have been researched by thinking of time delay as the bifurcation parameter. Besides, we calculate direction and stability of the Hopf bifurcation. Finally, we carry out some numerical simulations to prove the validity of theoretical results.

scholarly journals Bifurcation of a Cohen-Grossberg Neural Network with Discrete Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Qiming Liu ◽  
Wang Zheng
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Hopf Bifurcations ◽  
Bifurcation Parameter ◽  
Explicit Formulas ◽  
Global Hopf Bifurcation ◽  
Discrete Delays ◽  
Bifurcation And Stability

A simple Cohen-Grossberg neural network with discrete delays is investigated in this paper. The existence of local Hopf bifurcations is first considered by choosing the appropriate bifurcation parameter, and then explicit formulas are given to determine the direction of Hopf bifurcation and stability of the periodic solutions. Moreover, a set of sufficient conditions are given to guarantee the global Hopf bifurcation. Numerical simulations are given to illustrate the obtained results.

Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

2018 ◽  
Vol 28 (03) ◽  
pp. 1850042 ◽  
Author(s):  
Xin-You Meng ◽  
Yu-Qian Wu
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
State Feedback ◽  
Critical Value ◽  
Feedback Controller ◽  
Bifurcation Parameter ◽  
State Feedback Controller ◽  
Interior Equilibrium ◽  
Fish Model ◽  
Singularity Induced Bifurcation

In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

scholarly journals Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qingsong Liu ◽  
Yiping Lin ◽  
Jingnan Cao ◽  
Jinde Cao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Center Manifold ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Critical Value ◽  
Hopf Bifurcations ◽  
The Stability

The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosingτas bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.

Rank-One Chaos in a Periodically Kicked Three-Species Food Chain with Time-Delay

2020 ◽  
Vol 30 (03) ◽  
pp. 2050038
Author(s):  
Ping Yang ◽  
Juan Fang ◽  
Yunxian Dai ◽  
Yiping Lin
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Food Chain ◽  
Strange Attractor ◽  
Positive Equilibrium ◽  
Rank One ◽  
Delayed System

This paper is devoted to studying the problem of rank-one strange attractor in a three-species food chain with time-delay. The conditions for the existence of positive equilibrium and Hopf bifurcation are presented. By using the theory of rank-one maps formulated by Wang and Young in 2001, and then developed by us to the time-delayed system, the conditions for the system having rank-one strange attractor are obtained under periodically kicked system. Numerical simulations are presented to demonstrate the analytic results.

scholarly journals HOPF BIFURCATION ANALYSIS FOR A MATHEMATICAL MODEL OF P53-MDM2 INTERACTION

2008 ◽  
Vol 18 (01) ◽  
pp. 275-283 ◽  
Author(s):  
MIHAELA NEAMŢU ◽  
RAUL FLORIN HORHAT ◽  
DUMITRU OPRIŞ
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Stationary State ◽  
Bifurcation Analysis ◽  
Local Stability ◽  
Bifurcation Parameter ◽  
Simple Mathematical Model

In this paper we analyze a simple mathematical model which describes the interaction between proteins P53 and Mdm2. For the stationary state we discuss the local stability and the existence of a Hopf bifurcation. We study the direction and stability of the bifurcating periodic solutions by choosing the delay as a bifurcation parameter. Finally, we will offer some numerical simulations and present our conclusions.

scholarly journals Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-20
Author(s):  
Lingling Li ◽  
Jianwei Shen
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Bifurcation Theory ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Delay Model ◽  
Dynamical Behaviors ◽  
Theoretical Results

We focused on the gene regulative network involving Rb-E2F pathway and microRNAs (miR449) and studied the influence of time delay on the dynamical behaviors of Rb-E2F pathway by using Hopf bifurcation theory. It is shown that under certain assumptions the steady state of the delay model is asymptotically stable for all delay values; there is a critical value under another set of conditions; the steady state is stable when the time delay is less than the critical value, while the steady state is changed to be unstable when the time delay is greater than the critical value. Thus, Hopf bifurcation appears at the steady state when the delay passes through the critical value. Numerical simulations were presented to illustrate the theoretical results.

EFFECT OF AWARENESS PROGRAMS IN CONTROLLING THE PREVALENCE OF AN EPIDEMIC WITH TIME DELAY

2011 ◽  
Vol 19 (02) ◽  
pp. 389-402 ◽  
Author(s):  
A. K. MISRA ◽  
ANUPAMA SHARMA ◽  
VISHAL SINGH
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Stability Theory ◽  
Direct Contact ◽  
Behavioral Changes ◽  
Nonlinear Mathematical Model ◽  
Awareness Programs

A nonlinear mathematical model with delay to capture the dynamics of effect of awareness programs on the prevalence of any epidemic is proposed and analyzed. It is assumed that pathogens are transmitted via direct contact between susceptibles and infectives. It is assumed further that cumulative density of awareness programs increases at a rate proportional to the number of infectives. It is considered that awareness programs are capable of inducing behavioral changes in susceptibles, which result in the isolation of aware population. The model is analyzed using stability theory of differential equations and numerical simulations. The model analysis shows that, though awareness programs cannot eradicate infection, they help in controlling the prevalence of disease. It is also found that time delay in execution of awareness programs destabilizes the system and periodic solutions may arise through Hopf-bifurcation.

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