Hopf bifurcations in Lengyel–Epstein reaction–diffusion model with discrete time delay

We investigate bifurcations of the Lengyel–Epstein reaction–diffusion model involving time delay under the Neumann boundary conditions. Choosing the delay parameter as a bifurcation parameter, we show that Hopf bifurcation occurs. We also determine two properties of the Hopf bifurcation, namely dire...

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Bibliographic Details
Published in:Nonlinear dynamics 2015-02, Vol.79 (3), p.1757-1770
Main Authors: Merdan, H., Kayan, Ş.
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcation theory
Bifurcations
Boundary conditions
Canonical forms
Classical Mechanics
Control
Delay
Differential equations
Dynamical Systems
Economic models
Engineering
Hopf bifurcation
Manifolds
Mathematical models
Mechanical Engineering
Original Paper
Parameters
Stability
Time delay
Time lag
Vibration
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Summary:We investigate bifurcations of the Lengyel–Epstein reaction–diffusion model involving time delay under the Neumann boundary conditions. Choosing the delay parameter as a bifurcation parameter, we show that Hopf bifurcation occurs. We also determine two properties of the Hopf bifurcation, namely direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-014-1772-8