Jump transition due to a time‐dependent bifurcation parameter in the bistable ioadate–arsenous acid reaction

1989 ◽  
Vol 90 (11) ◽  
pp. 6129-6134 ◽  
Author(s):  
T. Erneux ◽  
J. P. Laplante
Keyword(s):  
Time Dependent ◽  
Bifurcation Parameter ◽  
Jump Transition ◽  
Acid Reaction

A Time-Dependent Bifurcation Model with Control and Pulsing Oscillations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4260-4266
Author(s):  
Qishao Lu ◽  
Cuncai Hua
Keyword(s):  
Control Problem ◽  
Memory Effects ◽  
Time Dependent ◽  
Bifurcation Parameter ◽  
Bifurcation Transition ◽  
Delayed Bifurcation ◽  
With Memory

A time-dependent bifurcation model and its control problem are studied. Firstly, the delayed bifurcating transition with memory effects due to time-dependent parameters are analysed. Secondly, a control problem with time-dependent parametric feedback in this bifurcation model is investigated. Finally, an important mechanism for pulsing oscillation is found as the result of the delayed bifurcation transition occurring when the bifurcation parameter varies periodically across the steady bifurcation value.

scholarly journals Dynamic transitions for the S-K-T competition system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ruikuan Liu ◽  
Dongpei Zhang
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary ◽  
Dynamical Behaviour ◽  
Critical Surface ◽  
Homogeneous State ◽  
Bifurcation Parameter ◽  
Continuous Transition ◽  
Dynamic Transition ◽  
Competition System ◽  
Jump Transition

<p style='text-indent:20px;'>This paper is concerned with dynamical transition for biological competition system modeled by the S-K-T equations. We study the dynamical behaviour of the S-K-T equations with two different boundary conditions. For the system under non-homogeneous Dirichlet boundary condition, we show that the system undergoes a mixed dynamic transition from the homogeneous state to steady state solutions when the bifurcation parameter cross the critical surface. For the system with Neumann boundary condition, we prove that the system undergoes a mixed dynamic transition, a jump transition and a continuous transition when the bifurcation parameter cross the critical number. Finally, two examples are provided to validate the effectiveness of the theoretical results.</p>

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