Synchronization-desynchronization Transitions Research Articles

Entangled chimeras in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, have been identified in various systems and generalized to coupled nonidentical oscillators. It has been shown that strong heterogeneity in the frequencies of nonidentical oscillators might be harmful to chimera states. In this work, we consider a ring of nonlocally coupled bicomponent phase oscillators in which two types of oscillators are randomly distributed along the ring: some oscillators with natural frequency ω1 and others with ω2. In this model, the heterogeneity in frequency is measured by frequency mismatch ∣ω1 − ω2∣ between the oscillators in these two subpopulations. We report that the nonlocally coupled bicomponent phase oscillators allow for chimera states no matter how large the frequency mismatch is. The bicomponent oscillators are composed of two chimera states, one supported by oscillators with natural frequency ω1 and the other by oscillators with natural frequency ω2. The two chimera states in two subpopulations are synchronized at weak frequency mismatch, in which the coherent oscillators in them share similar mean phase velocity, and are desynchronized at large frequency mismatch, in which the coherent oscillators in different subpopulations have distinct mean phase velocities. The synchronization-desynchronization transition between chimera states in these two subpopulations is observed with the increase in the frequency mismatch. The observed phenomena are theoretically analyzed by passing to the continuum limit and using the Ott-Antonsen approach.

Pattern formation and chimera states in 2D SQUID metamaterials.

The Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator with rich dynamical behavior, including chaos. When driven by a time-periodic magnetic flux, the SQUID exhibits extreme multistability at frequencies around the geometric resonance, which is manifested by a "snakelike" form of the resonance curve. Repeating motifs of SQUIDs form metamaterials, i.e., artificially structured media of weakly coupled discrete elements that exhibit extraordinary properties, e.g., negative diamagnetic permeability. We report on the emergent collective dynamics in two-dimensional lattices of coupled SQUID oscillators, which involves a rich menagerie of spatiotemporal dynamics, including Turing-like patterns and chimera states. Using Fourier analysis, we characterize these patterns and identify characteristic spatial and temporal periods. In the low coupling limit, the Turing-like patterns occur near the synchronization-desynchronization transition, which can be related to the bifurcation scenarios of the single SQUID. Chimeras emerge due to the multistability near the geometric resonance, and by varying the dc component of the external force, we can make them appear and reappear and, also, control their location. A detailed analysis of the parameter space reveals the coexistence of Turing-like patterns and chimera states in our model, as well as the ability to transform between these states by varying the system parameters.

Collective dynamics from stochastic thermodynamics

From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization–desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics.

Synchronization-desynchronization transitions in complex networks: an interplay of distributed time delay and inhibitory nodes.

We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart-Landau oscillators. To this end a symmetric network model is proposed for which the stability can be investigated analytically. It is found that beyond a critical inhibition ratio, synchronization tends to be unstable. However, increasing distributional widths can counteract this trend, leading to multiple resynchronization transitions at relatively high inhibition ratios. The extended applicability of the results is confirmed by numerical studies on asymmetrically perturbed network topologies. All investigations are performed on two distribution types, a uniform distribution and a Γ distribution.

On–off intermittent synchronization between two bidirectionally coupled double scroll circuits

In this report the intermittent route from full synchronization to full desynchronization, of two bidirectionally coupled, double-scroll circuits, was experimentally studied. Coupling resistance, between the two circuits, served as the bifurcation parameter, controlling the synchronization. It was shown that the synchronization–desynchronization transition was realized through a regime of incomplete synchronization of the on–off intermittency type.

Pattern formations in chaotic spatio-temporal systems

Pattern formations in chaotic spatio-temporal systems modelled by coupled chaotic oscillators are investigated. We focus on various symmetry breakings and different kinds of chaos synchronization-desynchronization transitions, which lead to certain types of spontaneous spatial orderings and the emergence of some typical ordered patterns, such as rotating wave patterns with splay phase ordering (orientational symmetry breaking) and partially synchronous standing wave patterns with in-phase ordering (translational symmetry breaking). General pictures of the global behaviors of pattern formations and transitions in coupled chaotic oscillators are provided.

Synchronized chaotic intermittent and spiking behavior in coupled map chains

We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks.

Experimental Chua-plasma phase synchronization of chaos.

Experimental phase synchronization of chaos is demonstrated for two different chaotic oscillators: a plasma discharge and the Chua circuit. Our technique includes real-time capability for observing synchronization-desynchronization transitions. This capability results from a strong combination of synchronization and control, and allows tuning adjustments for search and stabilization of synchronous states. A power law is observed for the mean time between 2pi phase slips for different coupling strenghts. The experimental results are consistent with the numerical simulations.

Transition to phase synchronization in coupled periodically driven chaotic pendulums.

We have studied the transition to phase synchronization in the system of two coupled periodically driven pendulums. For the case of identical units, the coupled system has an infinite number of invariant subspaces. The synchronization-desynchronization transition is at the blowout bifurcation which coincides with the hyperchaos-chaos transition. On-off intermittency and intermingled basins of attraction can be observed close to this transition. For the case of nonidentical pendulums, the synchronization-desynchronization transition occurs far beyond the hyperchaos-chaos transition. The basin structure and the statistics of the accompanying intermittency are different from those for identical units.