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.
The phenomenon of emergent amplified response is reported in two unidirectionally coupled identical chaotic systems when heterogeneity as a parameter mismatch is introduced in a state of complete synchrony. The amplified response emerges from the interplay of heterogeneity and a type of cross-feedback coupling. It is reflected as an expansion of the response attractor in some directions in the state space of the coupled system. The synchronization manifold is simply rotated by the parameter detuning while its stability in the transverse direction is still maintained. The amplification factor is linearly related to the amount of parameter detuning. The phenomenon is elaborated with examples of the paradigmatic Lorenz system, the Shimizu-Morioka single-mode laser model, the Rössler system, and a Sprott system. Experimental evidence of the phenomenon is obtained in an electronic circuit. The method may provide an engineering tool for distortion-free amplification of chaotic signals.
In this paper, we introduce the concept of totally supra N-continuous function and totally supra N-closed map and investigated the relationship of these funct
In this paper we introduce (I, γ)-generalized semi-closed sets in topological spaces and also introduce γS − T I -spaces and investigate some of their properties.
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