Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102 (United States)
We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.
- OSTI ID:
- 21464505
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevE.82.036601; (c) 2010 The American Physical Society; ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
BIFURCATION
COMPUTERIZED SIMULATION
CONTROL SYSTEMS
COUPLING
DIFFUSION
FAILURES
FEEDBACK
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
STABILITY
TIME DELAY
TWO-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
SIMULATION