Complex localization mechanisms in networks of coupled oscillators: two case studies
arXiv:2309.08547 · doi:10.1063/5.0174550
Abstract
Localized phenomena abound in nature and throughout the physical sciences. Some universal mechanisms for localization have been characterized, such as in the snaking bifurcations of localized steady states in pattern-forming partial differential equations. While much of this understanding has been targeted at steady states, recent studies have noted complex dynamical localization phenomena in systems of coupled oscillators. These localized states can come in the form of symmetry-breaking chimera patterns that exhibit a coexistence of coherence and incoherence in symmetric networks of coupled oscillators and gap solitons emerging in the band gap of parametrically driven networks of oscillators. Here, we report detailed numerical continuations of localized time-periodic states in systems of coupled oscillators, while also documenting the numerous bifurcations they give way to. We find novel routes to localization involving bifurcations of heteroclinic cycles in networks of Janus oscillators and strange bifurcation diagrams resembling chaotic tangles in a parametrically driven array of coupled pendula. We highlight the important role of discrete symmetries and the symmetric branch points that emerge in symmetric models.
arXiv comment15 pages, 9 figures
References in corpus (25)
- Chimera States for Coupled Oscillators
- Discrete Breathers
- Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
- Non-reciprocal phase transitions
- Mathematical frameworks for oscillatory network dynamics in neuroscience
- Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
- Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
- Chimeras in networks with purely local coupling
- Phase-amplitude descriptions of neural oscillator models
- Self-induced switchings between multiple space-time patterns on complex networks of excitable units
- Heteroclinic switching between chimeras
- Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift-Hohenberg equation as an example
- Critical Switching in Globally Attractive Chimeras
- Dark solitons, modulation instability and breathers in a chain of weakly non-linear oscillators with cyclic symmetry
- Spatially Localized Structures in Lattice Dynamical Systems
- Anharmonic classical time crystals: A coresonance pattern formation mechanism
- Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems
- Heterogeneity-stabilized homogeneous states in driven media
- Multifaceted dynamics of Janus oscillator networks
- Localized patterns in planar bistable weakly coupled lattice systems
- Nucleation and propagation of excitation fronts in self-excited systems
- Isolas of multi-pulse solutions to lattice dynamical systems
- Snaking bifurcations of localized patterns on ring lattices
- Standing Wave Solutions in Twisted Multicore Fibers
- Collisions of localized patterns in a nonvariational Swift-Hohenberg equation