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This contribution is devoted to the study of the collective behavior of two HR neurons followed by a network of HR neurons. The collective behavior of the two coupled neuron was obtained from the connection between the traditional 3D HR and a memristive 2D HR neuron via a gap junction. The dynamical properties of this rst topology revealed that it is dissipative therefore can support complex phenomena. From numerical simulations, it is found that the coupled neurons display a variety of behaviors just by varying the control parameter. Amongst these behaviors found, we have periodic bursting or spiking, quasi-periodic bursting or spiking, and chaotic bursting or spiking. Non-synchronized motion is observed when the electrical coupling strength is weak. However, synchronized cluster states are observed when the coupling strength is increased. Also varied of cross ring networks made of combination of N = 100 these different HR neurons in the network are also investigated. It is discovered that the spatiotemporal patterns are affected by the network topology. The cluster states are represented in the non- homogenous network's ring and star structures. The ring and ring-star structures contain single and double-well chimera states. Finally, in the PSIM simulation environment, a comparable electronic circuit for the two coupled heterogeneous neurons is designed and investigated. The results obtained from the designed analog circuit and the mathematical model of the two coupled neurons match perfectly.

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In this article, we have studied a [Formula: see text]D map, which is formed by combining the two well-known maps, i.e. the tent and the logistic maps in the unit interval, i.e. [Formula: see text]. The point of discontinuity of the map (known as border) denotes the transition from tent map to logistic map. The proposed map can behave as the piecewise smooth or nonsmooth map or both (depending on the behavior of the map just before and after the border) and the dynamics of the map has been studied using analytical tools and numerical simulations. Characterization has been done by primarily studying the Lyapunov exponents and the corresponding bifurcation diagrams. Some peculiar dynamics of this map have been shown numerically. Finally, a Simulink implementation of the proposed map has been demonstrated.

Robust Chaos occurring in piecewise smooth dynamical systems is very important in practical applications. It is defined by the absence of periodic windows and coexisting attractors in some neighbourhood of the parameter space. In earlier works, the occurrence of robust chaos was reported in the context of piecewise linear 1D and 2D maps, and regions of occurrences have been investigated in 1D and 2D switching circuits. Here, it has been reported the first experimental observation of this phenomenon in a 3D electronic switching system and obtain the region of parameter space by constructing a discrete map of the system.