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Localized structures in nonlinear lattices with diffusive coupling and external driving

Mitkov1, Kladko, Bishop

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
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Discreteness stabilizes localized structures in nonlinear lattices. In an external field, these structures can destabilize, leading to homogeneous states or front nucleation, as confirmed by analytic and numerical methods.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Lattice dynamics

Background:

  • Localized structures in nonlinear systems are crucial for information propagation.
  • Discreteness in lattices can significantly alter the stability of these structures.
  • Understanding stability under external fields is key to controlling system behavior.

Purpose of the Study:

  • To investigate the stabilizing effect of discreteness on localized structures in one-dimensional nonlinear lattices.
  • To analyze the loss of stability of these structures when subjected to an external driving field.
  • To characterize the bifurcation mechanisms and singularities involved.

Main Methods:

  • Analytical derivation of stability conditions.
  • Numerical simulations of lattice dynamics.

Related Experiment Videos

  • Bifurcation analysis to identify critical phenomena.

    • Main Results:

    • Discreteness enhances the stability of localized structures.
    • External driving fields can induce instability, leading to either homogeneous states or front nucleation.
    • A cusp singularity was identified in the bifurcation diagram.

    Conclusions:

    • The interplay between discreteness and external fields dictates the stability of localized structures.
    • The observed instabilities provide insights into pattern formation and pattern destruction in discrete nonlinear systems.
    • Analytic and numerical results show strong quantitative agreement, validating the theoretical framework.