Synchronization of spatially extended chaotic systems in the presence of asymmetric coupling

Amplitude death in a pair of one-dimensional complex Ginzburg-Landau systems coupled by diffusive connections

This paper shows that, in a pair of one-dimensional complex Ginzburg-Landau (CGL) systems, diffusive connections can induce amplitude death. Stability analysis of a spatially uniform steady state in coupled CGL systems reveals that amplitude death never occurs in a pair of identical CGL systems coupled by no-delay connection, but can occur in the case of delay connection. Moreover, amplitude death never occurs in coupled identical CGL systems with zero nominal frequency. Based on these analytical results, we propose a procedure for designing the connection delay time and the coupling strength to induce spatial-robust stabilization, that is, a stabilization of the steady state for any system size and any boundary condition. Numerical simulations are performed to confirm the analytical results.

Oscillation death in asymmetrically delay-coupled oscillators

Symmetrically coupled oscillators represent a limiting case for studying the dynamics of natural systems. Therefore, we here investigate the effect of coupling asymmetry on delay-induced oscillation death (OD) in coupled nonlinear oscillators. It is found that the asymmetrical coupling substantially enlarges the domain of the OD island in the parameter space. Specifically, when the intensity of asymmetry is enhanced by turning down the value of the coupling asymmetry parameter α, the OD island gradually expands along two directions of both the coupling delay and the coupling strength. The expansion behavior of the OD region is well characterized by a power law scaling, R=α(γ) with γ≈-1.19. The minimum value of the intrinsic frequency, for which OD is possible, monotonically decreases with decreasing α and saturates around a constant value in the limit of α→0. The generality of the conducive effect of coupling asymmetry is confirmed in a numerical study of two delay-coupled chaotic Rössler oscillators. Our findings shed an improved light on the understanding of dynamics in asymmetrically delay-coupled systems.

Pattern formation of coupled spiral waves in bilayer systems: rich dynamics and high-frequency dominance

The interaction of two spiral waves with independent frequencies in a bilayer oscillatory medium (one spiral in each layer) and with a symmetric coupling e is studied. If the spirals have different frequencies, the faster spiral is unaffected by the slower one, and the slower can show a variety of behaviors, which depend on e and include, in order of increasing e, phase drifting, amplitude modulation, amplitude domination, and phase synchronization. This high-frequency dominance, the asymmetric driving-response effect under the condition of a symmetric coupling, is generic and independent of whether the coupled spiral waves are outwardly rotating or inwardly rotating spirals. If the spirals have identical frequencies, they may even show complete synchronization, parallel drift, or circular drift, depending on the relative rotation direction of the two spirals and their initial separation distance. Comparisons with coupled spirals in monolayer media, previous works on coupled spirals in bilayer systems, and coupled phase oscillators are made.

Novel type of amplitude spiral wave in a two-layer system

Interaction of spiral waves in a two-layer system described by a model of coupled complex Ginzburg-Landau equations with negative-feedback couplings ε(1) and ε(2) is studied. Synchronization of two spiral waves can be broadly found if ε(1)+ε(2) is sufficiently large. Prior to the synchronization, under the condition of strongly asymmetric coupling (∣ε(1)-ε(2)∣≫0), a novel type of spiral wave, amplitude spiral wave, exists in the driven system. The pattern of amplitude spiral wave shows the spiral in the amplitude and without a singularity point (tip), compared to usual spiral waves known for phase with amplitude uniform far away from tips and rotating around tips.

Generalized synchronization in coupled Ginzburg-Landau equations and mechanisms of its arising

Generalized chaotic synchronization regime is observed in the unidirectionally coupled one-dimensional Ginzburg-Landau equations. The mechanism resulting in the generalized synchronization regime arising in the coupled spatially extended chaotic systems demonstrating spatiotemporal chaotic oscillations has been described. The cause of the generalized synchronization occurrence is studied with the help of the modified Ginzburg-Landau equation with additional dissipation.

Synchronization in complex networks with age ordering

The propensity for synchronization is studied in a complex network of asymmetrically coupled units, where the asymmetry in a given link is determined by the relative age of the involved nodes. In growing scale-free networks, synchronization is enhanced when couplings from older to younger nodes are dominant. We describe the requirements for such an effect in a more general context and compare with the situations in nongrowing random networks with and without a degree ordering.