We present evidence of extreme events in two Hindmarsh-Rose (HR) bursting neurons mutually interacting via two different coupling configurations: chemical synaptic- and gap junctional-type diffusive coupling. A dragon-king-like probability distribution of the extreme events is seen for combinations of synaptic coupling where small- to medium-size events obey a power law and the larger events that cross an extreme limit are outliers. The extreme events originate due to instability in antiphase synchronization of the coupled systems via two different routes, intermittency and quasiperiodicity routes to complex dynamics for purely excitatory and inhibitory chemical synaptic coupling, respectively. For a mixed type of inhibitory and excitatory chemical synaptic interactions, the intermittency route to extreme events is only seen. Extreme events with our suggested distribution is also seen for gap junctional-type diffusive, but repulsive, coupling where the intermittency route to complexity is found. A simple electronic experiment using two diffusively coupled analog circuits of the HR neuron model, but interacting in a repulsive way, confirms occurrence of the dragon-king-like extreme events.
We observe chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (called as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. Interestingly, we also recorded a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrates from one to another population. To test the generality of the coupling configuration, we present another example of bistable system, the van der Pol-Duffing system where the chimeralike states are observed, however, the coherent population is periodic or quasiperiodic and the incoherent population is of chaotic in nature. Furthermore, we apply the coupling to a network of chaotic Rössler system where we find the chaos-chaos chimeralike states.
Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and continues for a range of parameter values. Three important processes of instabilities, namely, interior crisis, Pomeau–Manneville intermittency, and the breakdown of quasiperiodic motion, are most common as observed in many systems that lead to such occasional and rare transitions to large amplitude spiking events. We characterize these occasional large events as extreme events if they are larger than a statistically defined significant height. We present two exemplary systems, a single system and a coupled system, to illustrate how the instabilities work to originate extreme events and they manifest as non-trivial dynamical events. We illustrate the dynamical and statistical properties of such events.
We report rare and recurrent large spiking events in a heterogeneous network of superconducting Josephson junctions (JJ) connected through a resistive load and driven by a radio-frequency (rf) current in addition to a constant bias. The intermittent large spiking events show characteristic features of extreme events (EE) since they are larger than a statistically defined significant height. Under the influence of repulsive interactions and an impact of heterogeneity of damping parameters, the network splits into three sub-groups of junctions, one in incoherent rotational, another in coherent librational motion and a third sub-group originating EE. We are able to scan the whole population of junctions with their distinctive individual dynamical features either in EE mode or non-EE mode in parameter space. EE migrates spatially from one to another sub-group of junctions depending upon the repulsive strength and the damping parameter. For a weak repulsive coupling, all the junctions originate frequent large spiking events, in rotational motion when the average inter-spike-interval (ISI) is small, but it increases exponentially with repulsive interaction; it largely deviates from its exponential growth at a break point where EE triggers in a sub-group of junctions. The probability density of inter-event-intervals (IEI) in the subgroup exhibits a Poisson distribution. EE originates via bubbling instability of in-phase synchronization.
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