Nonequilibrium potential for arbitrary-connected networks of FitzHugh–Nagumo elements

2010 ◽  
Vol 389 (9) ◽  
pp. 1931-1944 ◽  
Author(s):  
Alejandro D. Sánchez ◽  
Gonzalo G. Izús
Keyword(s):  
Nonequilibrium Potential

Critical Slowing-Down of Spatially Nonhomogeneous Patterns in a Reaction–Diffusion Model

1997 ◽  
Vol 11 (14) ◽  
pp. 1717-1730 ◽  
Author(s):  
Fernando Castelpoggi ◽  
Horacio S. Wio ◽  
Damian H. Zanette
Keyword(s):  
Diffusion Model ◽  
Lyapunov Functional ◽  
Reaction Diffusion ◽  
Critical Slowing Down ◽  
Threshold Parameter ◽  
Extended System ◽  
Slowing Down ◽  
Reaction Diffusion Model ◽  
Spatially Extended ◽  
Nonequilibrium Potential

We exploit the concept of the nonequilibrium potential in order to analize the approach to stationary homogeneous and nonhomogeneous equilibrium states in a bounded bistable reaction-diffusion model. The analysis proceeds through the study of the Lyapunov functional, in terms of a control parameter -the threshold parameter ϕc-in the neighbourghood of a critical point (where a stable and an unstable pattern coalesce), that clearly shows the phenomenon of critical slowing-down in a spatially extended system.

Large Fluctuations in a Periodically Driven Dynamical System

1998 ◽  
Vol 08 (04) ◽  
pp. 747-754 ◽  
Author(s):  
M. I. Dykman ◽  
V. N. Smelyanskiy ◽  
D. G. Luchinsky ◽  
R. Mannella ◽  
P. V. E. McClintock ◽  
...  
Keyword(s):  
Noise Intensity ◽  
Low Noise ◽  
Coordinate Space ◽  
Stable States ◽  
Small Noise ◽  
Periodically Driven ◽  
Optimal Paths ◽  
Electronic Model ◽  
Large Fluctuations ◽  
Nonequilibrium Potential

Fluctuations in a periodically driven overdamped oscillator are studied theoretically and experimentally in the limit of low noise intensity by investigation of their prehistory. It is shown that, for small noise intensity, fluctuations to points in coordinate space that are remote from the stable states occur along paths that form narrow tubes. The tubes are centered on the optimal paths corresponding to trajectories of an auxiliary Hamiltonian system. The optimal paths themselves, and the tubes of paths around them, are visualized through measurements of the prehistory probability distribution for an electronic model. Some general features of fluctuations in nonequilibrium systems, such as singularities in the pattern of optimal paths, the corresponding nondifferentiability of the generalized nonequilibrium potential, and the feasibility of their experimental investigation, are discussed.

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