scholarly journals Global Hopf bifurcation of a delayed phytoplankton-zooplankton system considering toxin producing effect and delay dependent coefficient

2019 ◽  
Vol 16 (5) ◽  
pp. 3807-3829 ◽  
Author(s):  
Zhichao Jiang ◽  
◽  
Xiaohua Bi ◽  
Tongqian Zhang ◽  
B.G. Sampath Aruna Pradeep ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Global Hopf Bifurcation ◽  
Delay Dependent

Global Hopf Bifurcation in a Phytoplankton–Zooplankton System with Delay and Diffusion

2021 ◽  
Vol 31 (08) ◽  
pp. 2150114
Author(s):  
Ming Liu ◽  
Jun Cao ◽  
Xiaofeng Xu
Keyword(s):  
Hopf Bifurcation ◽  
Global Existence ◽  
Upper And Lower Solutions ◽  
Positive Periodic Solutions ◽  
Global Hopf Bifurcation ◽  
System With Delay ◽  
Local Hopf Bifurcation ◽  
Distribution Of Eigenvalues ◽  
The Stability ◽  
And Diffusion

In this paper, the dynamics of a phytoplankton–zooplankton system with delay and diffusion are investigated. The positivity and persistence are studied by using the comparison theorem and upper and lower solutions method. The stability of steady states and the existence of local Hopf bifurcation are obtained by analyzing the distribution of eigenvalues. And the global existence of positive periodic solutions is established by using the global Hopf bifurcation result given by Wu [1996]. Finally, some numerical simulations are carried out to illustrate the analytical 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.

Global Hopf Bifurcation in a Simple Climate Model

1983 ◽  
Vol 43 (5) ◽  
pp. 1019-1041 ◽  
Author(s):  
Michael Ghil ◽  
John Tavantzis
Keyword(s):  
Hopf Bifurcation ◽  
Climate Model ◽  
Global Hopf Bifurcation ◽  
Simple Climate Model

DOUBLE HOPF BIFURCATION FOR STUART–LANDAU SYSTEM WITH NONLINEAR DELAY FEEDBACK AND DELAY-DEPENDENT PARAMETERS

2007 ◽  
Vol 10 (04) ◽  
pp. 423-448 ◽  
Author(s):  
SUQI MA ◽  
QISHAO LU ◽  
S. JOHN HOGAN
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Resonant Oscillation ◽  
Double Hopf Bifurcation ◽  
Dependent Parameter ◽  
Stable Periodic ◽  
Delay Feedback Control ◽  
Delay Dependent ◽  
Nonlinear Delay

A Stuart–Landau system under delay feedback control with the nonlinear delay-dependent parameter e-pτ is investigated. A geometrical demonstration method combined with theoretical analysis is developed so as to effectively solve the characteristic equation. Multi-stable regions are separated from unstable regions by allocations of Hopf bifurcation curves in (p,τ) plane. Some weak resonant and non-resonant oscillation phenomena induced by double Hopf bifurcation are discovered. The normal form for double Hopf bifurcation is deduced. The local dynamical behavior near double Hopf bifurcation points are also clarified in detail by using the center manifold method. Some states of two coexisting stable periodic solutions are verified, and some torus-broken procedures are also traced.

Sign in / Sign up

Export Citation Format

Share Document