Chimera patterns and subthreshold oscillations in two-dimensional networks of fractally coupled leaky integrate-and-fire neurons

Multistable Synaptic Plasticity Induces Memory Effects and Cohabitation of Chimera and Bump States in Leaky Integrate-and-Fire Networks

Chimera states and bump states are collective synchronization phenomena observed independently (in different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of coherent and incoherent domains, bump states consist of alternating active and inactive domains. The idea of multistable plasticity in the network connections originates from brain dynamics where the strength of the synapses (axons) connecting the network nodes (neurons) may change dynamically in time; when reaching the steady state the network connections may be found in one of many possible values depending on various factors, such as local connectivity, influence of neighboring cells etc. The sign of the link weights is also a significant factor in the network dynamics: positive weights are characterized as excitatory connections and negative ones as inhibitory. In the present study we consider the simplest case of bistable plasticity, where the link dynamics has only two fixed points. During the system/network integration, the link weights change and as a consequence the network organizes in excitatory or inhibitory domains characterized by different synaptic strengths. We specifically explore the influence of bistable plasticity on collective synchronization states and we numerically demonstrate that the dynamics of the linking may, under special conditions, give rise to co-existence of bump-like and chimera-like states simultaneously in the network. In the case of bump and chimera co-existence, confinement effects appear: the different domains stay localized and do not travel around the network. Memory effects are also reported in the sense that the final spatial arrangement of the coupling strengths reflects some of the local properties of the initial link distribution. For the quantification of the system's spatial and temporal features, the global and local entropy functions are employed as measures of the network organization, while the average firing rates account for the network evolution and dynamics. In particular, the spatial minima of the local entropy designate the transition points between domains of different synaptic weights in the hybrid states, while the number of minima corresponds to the number of different domains. In addition, the entropy deviations signify the presence of chimera-like or bump-like states in the network.

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.

Alternating activity patterns and a chimeralike state in a network of globally coupled excitable Morris-Lecar neurons

Spatiotemporal chaos collapses to either a rest state or a propagating pulse in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Adding global varying synaptic coupling to the ring network reveals complex transient behavior. Spatiotemporal chaos collapses into a transient pulse that reinitiates spatiotemporal chaos to allow sequential pattern switching until a collapse to the rest state. A domain of irregular neuron activity coexists with a domain of inactive neurons forming a transient chimeralike state. Transient spatial localization of the chimeralike state is observed for stronger synapses.