The effect of diffusion on the Hopf bifurcation in a model chemical reaction exhibiting oscillatory behavior

1991 ◽  
Vol 94 (10) ◽  
pp. 6807-6810
Author(s):  
Arun K. Dutt
Keyword(s):  
Hopf Bifurcation ◽  
Chemical Reaction ◽  
Oscillatory Behavior ◽  
Model Chemical Reaction

scholarly journals An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

2017 ◽  
Vol 24 (3) ◽  
pp. 419-433
Author(s):  
Valentina Castellanos-Rodríguez ◽  
Eric Campos-Cantón ◽  
Rafael Barboza-Gudiño ◽  
Ricardo Femat
Keyword(s):  
Hopf Bifurcation ◽  
Oscillatory Behavior ◽  
Block Model ◽  
Complex Dynamic ◽  
Seismic Parameters ◽  
Bifurcation Mechanism ◽  
Sustained Oscillations ◽  
Upper Limit ◽  
Slow Earthquakes ◽  
Frictional Coefficients

Abstract. The complex oscillatory behavior of a spring-block model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich–Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone – where slow earthquakes are generated within the frictionally unstable region – is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration.

Hopf bifurcation and multiple limit cycles in bio-chemical reaction of the morphogenesis process

2009 ◽  
Vol 47 (2) ◽  
pp. 739-749
Author(s):  
Siyuan Wang ◽  
Xuncheng Huang ◽  
Lemin Zhu ◽  
Minaya Villasana
Keyword(s):  
Hopf Bifurcation ◽  
Chemical Reaction ◽  
Limit Cycles

scholarly journals ON DIFFUSION DRIVEN OSCILLATIONS IN COUPLED DYNAMICAL SYSTEMS

1999 ◽  
Vol 09 (04) ◽  
pp. 629-644 ◽  
Author(s):  
ALEXANDER POGROMSKY ◽  
TORKEL GLAD ◽  
HENK NIJMEIJER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Threshold Value ◽  
Oscillatory Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonminimum Phase ◽  
Nonminimum Phase Systems ◽  
Diffusive Medium ◽  
Phase Systems

The paper deals with the problem of destabilization of diffusively coupled identical systems. Following a question of Smale [1976], it is shown that globally asymptotically stable systems being diffusively coupled, may exhibit oscillatory behavior. It is shown that if the diffusive medium consists of hyperbolically nonminimum phase systems and the diffusive factors exceed some threshold value, the origin of the overall system undergoes a Poincaré–Andronov–Hopf bifurcation resulting in oscillatory behavior.

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