scholarly journals HOPF bifurcation and stability conditions for a class of nonlinear mass regulation systems with delay

2021 ◽  
Vol 238 ◽  
pp. 109665
Author(s):  
Wen-qing Zhang ◽  
Liang-long Da ◽  
Qin-dong Sun ◽  
Lin Zhang ◽  
Wu-hong Guo
Keyword(s):  
Hopf Bifurcation ◽  
Stability Conditions ◽  
Bifurcation And Stability

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.

Hopf Bifurcation Induced by Delay Effect in a Diffusive Tumor-Immune System

2018 ◽  
Vol 28 (11) ◽  
pp. 1850136 ◽  
Author(s):  
Ben Niu ◽  
Yuxiao Guo ◽  
Yanfei Du
Keyword(s):  
Immune System ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Center Manifold ◽  
Immune Cell ◽  
Tumor Treatment ◽  
Delay Effect ◽  
Stable Periodic ◽  
The Stability ◽  
Bifurcation And Stability

Tumor-immune interaction plays an important role in the tumor treatment. We analyze the stability of steady states in a diffusive tumor-immune model with response and proliferation delay [Formula: see text] of immune system where the immune cell has a probability [Formula: see text] in killing tumor cells. We find increasing time delay [Formula: see text] destabilizes the positive steady state and induces Hopf bifurcations. The criticality of Hopf bifurcation is investigated by deriving normal forms on the center manifold, then the direction of bifurcation and stability of bifurcating periodic solutions are determined. Using a group of parameters to simulate the system, stable periodic solutions are found near the Hopf bifurcation. The effect of killing probability [Formula: see text] on Hopf bifurcation values is also discussed.

scholarly journals A nonlinear two-species oscillatory system: bifurcation and stability analysis

2003 ◽  
Vol 2003 (31) ◽  
pp. 1981-1991 ◽  
Author(s):  
Malay Bandyopadhyay ◽  
Rakhi Bhattacharya ◽  
C. G. Chakrabarti
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Wave Train ◽  
Oscillatory System ◽  
Homogeneous System ◽  
Travelling Wave ◽  
Chemical System ◽  
Oscillatory Chemical ◽  
Bifurcation And Stability

The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.

scholarly journals Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

2019 ◽  
Vol 17 (1) ◽  
pp. 141-159 ◽  
Author(s):  
Zaowang Xiao ◽  
Zhong Li ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Bifurcation And Stability

Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.

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.

scholarly journals Hopf Bifurcation Analysis and Anticontrol of Hopf Circles of the Rössler-Like System

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Ranchao Wu ◽  
Xiang Li
Keyword(s):  
Hopf Bifurcation ◽  
Projective Synchronization ◽  
Linear Feedback ◽  
Normal Form Theory ◽  
Dynamical Behaviors ◽  
Control Scheme ◽  
Stable Periodic ◽  
Form Theory ◽  
Synchronization Scheme ◽  
Bifurcation And Stability

A new Rössler-like system is constructed by the linear feedback control scheme in this paper. As well, it exhibits complex dynamical behaviors, such as bifurcation, chaos, and strange attractor. By virtue of the normal form theory, its Hopf bifurcation and stability are investigated in detail. Consequently, the stable periodic orbits are bifurcated. Furthermore, the anticontrol of Hopf circles is achieved between the new Rössler-like system and the original Rössler one via a modified projective synchronization scheme. As a result, a stable Hopf circle is created in the controlled Rössler system. The corresponding numerical simulations are presented, which agree with the theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document