scholarly journals Stability analysis and Hopf bifurcation in a diffusive epidemic model with two delays

2020 ◽  
Vol 17 (4) ◽  
pp. 4127-4146
Author(s):  
Huan Dai ◽  
◽  
Yuying Liu ◽  
Junjie Wei ◽  
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Epidemic Model ◽  
Two Delays

scholarly journals Dynamics and Stability Analysis of a Brucellosis Model with Two Discrete Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Paride O. Lolika ◽  
Steady Mushayabasa
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Incubation Period ◽  
Steady States ◽  
Discrete Delays ◽  
Two Delays

We present a mathematical model for brucellosis transmission that incorporates two discrete delays and culling of infected animals displaying signs of brucellosis infection. The first delay represents the incubation period while the second account for the time needed to detect and cull infectious animals. Feasibility and stability of the model steady states have been determined analytically and numerically. Further, the occurrence of Hopf bifurcation has been established. Overall the findings from the study, both analytical and numerical, suggest that the two delays can destabilize the system and periodic solutions can arise through Hopf bifurcation.

On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 2: Nonautonomous System

1999 ◽  
Vol 121 (1) ◽  
pp. 105-109 ◽  
Author(s):  
M. Moh’d ◽  
K. Huseyin
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Autonomous System ◽  
Critical Value ◽  
Harmonic Excitation ◽  
Nonautonomous System ◽  
External Excitation ◽  
Zero Eigenvalue ◽  
Bifurcation And Stability

This paper extends the bifurcation and stability analysis of the autonomous system considered in Part 1 to the case of a corresponding nonautonomous system. The effect of an external harmonic excitation on the Hopf bifurcation is studied via a modified Intrinsic Harmonic Balancing technique. It is observed that a shift in the critical value of the parameter occurs due to the external excitation. The analysis is carried out with the aid of MAPLE which is also instrumental in verifying the consistency of the approximations conveniently.

A NONLINEAR DELAY MODEL DESCRIBING THE GROWTH OF TUMOR CELLS UNDER IMMUNE SURVEILLANCE AGAINST CANCER AND ITS STABILITY ANALYSIS

2012 ◽  
Vol 05 (03) ◽  
pp. 1260017 ◽  
Author(s):  
LING CHEN ◽  
WANBIAO MA
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Tumor Cells ◽  
Local Stability ◽  
Immune Surveillance ◽  
Delay Model ◽  
Existence Of Periodic Solutions ◽  
Growth Of Tumor ◽  
Nonlinear Delay

In this paper, based on some biological meanings and a model which was proposed by Lefever and Garay (1978), a nonlinear delay model describing the growth of tumor cells under immune surveillance against cancer is given. Then, boundedness of the solutions, local stability of the equilibria and Hopf bifurcation of the model are discussed in details. The existence of periodic solutions explains the restrictive interactions between immune surveillance and the growth of the tumor cells.

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.

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