Stability and Hopf bifurcation for an epidemic disease model with time delay

2017 ◽  
Author(s):  
Yuguang Wang ◽  
Yanan Li ◽  
Wenshuai Wang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Disease Model ◽  
Epidemic Disease

Stability and Hopf bifurcation for an epidemic disease model with delay

2006 ◽  
Vol 30 (1) ◽  
pp. 204-216 ◽  
Author(s):  
Chengjun Sun ◽  
Yiping Lin ◽  
Maoan Han
Keyword(s):  
Hopf Bifurcation ◽  
Disease Model ◽  
Epidemic Disease

scholarly journals Dynamical analysis of a giving up smoking model with time delay

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zizhen Zhang ◽  
Ruibin Wei ◽  
Wanjun Xia
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory

AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.

Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term

2018 ◽  
Vol 313 ◽  
pp. 306-315 ◽  
Author(s):  
Swati Tyagi ◽  
Subit K Jain ◽  
Syed Abbas ◽  
Shahlar Meherrem ◽  
Rajendra K Ray
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Network Model ◽  
Bifurcation Analysis ◽  
Reaction Diffusion ◽  
Neuron Network ◽  
Diffusion Term

scholarly journals Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Wanjun Xia ◽  
Soumen Kundu ◽  
Sarit Maitra
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Center Manifold ◽  
Transmission Rate ◽  
Sufficient Conditions ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Ratio Dependent ◽  
Theoretical Results

A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.

DYNAMICS AND DOUBLE HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY

2009 ◽  
Vol 19 (11) ◽  
pp. 3733-3751 ◽  
Author(s):  
SUQI MA ◽  
ZHAOSHENG FENG ◽  
QISHAI LU
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Center Manifold ◽  
Hopf Bifurcations ◽  
Value Of Time ◽  
Asymptotically Stable ◽  
Universal Unfolding ◽  
Double Hopf Bifurcation ◽  
Bifurcation Points ◽  
The Rose

In this paper, we are concerned with the Rose–Hindmarsh model with time delay. By applying the generalized Sturm criterion, a number of imaginary roots of the characteristic equation are classified. The absolutely stable regions for any value of time delay are detected. By the continuous software DDE-Biftool, both the Hopf bifurcation curves and double Hopf bifurcation points are illustrated in parametric spaces. The normal form and universal unfolding at double Hopf bifurcation points are considered by the center manifold method. Some examples also indicate that the corresponding unique attractor near each double Hopf point is asymptotically stable.

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