Wave trains, self-oscillations and synchronization in discrete media

2005/06/06 by A. Carpio · 1 citation
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #cond-mat.other #stochastic dynamics and bifurcation

paper · pdf · doi:10.1016/j.physd.2005.06.004

to appear in Physica D: Nonlinear Phenomena

arxiv created 2005/06/06 · openalex publication_date 2005/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated firing at a boundary. In self-oscillatory media, wave trains persist but synchronization phenomena arise. An equation describing the evolution of the oscillator phases is derived.

Citations

• Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells
• Impulses and Physiological States in Theoretical Models of Nerve Membrane
• Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems
• Theory of crystal growth and interface motion in crystalline materials
• Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium

Cited by

• Photoexcited semiconductor superlattices as constrained excitable media: Motion of dipole domains and current self-oscillations