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5. Complex dynamics of a heterogeneous network of Hindmarsh-Rose neurons

Author

Njitacke, Zeric Tabekoueng, Muni, Sishu Shankar, Seth, Soumyajit, Awrejcewicz, Jan, and Kengne, Jacques

Subjects
Quantitative Biology - Neurons and Cognition, Nonlinear Sciences - Chaotic Dynamics
Abstract

In this contribution, we have considered the collective behavior of the two as well as the network of heterogeneous coupled Hindmarsh Rose (HR) neurons. The heterogeneous models were made of a memristive 2D (HR) and the traditional 3D HR neurons. Investigating a model of two coupled neurons through an electrical synapse reveals dissipative properties. When control parameters are varied, the coupled neuron model exhibits rich dynamics, such as the periodic, quasi-periodic, and chaotic dynamics involving either bursting or spiking oscillations. For weak electrical coupling strength, non-synchronized motion is observed. But in the case of higher coupling strength, synchronized cluster states are observed. Besides, ring-star networks of up to 100 under three different heterogeneous topologies are being investigated, and various spatiotemporal patterns are explored. It is found that the spatiotemporal patterns depend on the topology of the heterogeneous network considered. A new clustered chimera state is revealed qualitatively via the recurrence plot. The cluster states are indicated in the ring and star configurations of the heterogeneous network. Single and double-well chimera states have been revealed in the ring and ring-star structures. Finally, an equivalent electronic circuit for the two coupled heterogeneous is designed and investigated in the PSIM simulation environment. A perfect match is observed between the results obtained from the designed analog circuit and the mathematical model of the two coupled neurons, which supports the fact that our obtained results are not related to an artifact.

Published
2022
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23. Dynamical Analysis and Offset Boosting in a 4-Dimensional Quintic Chaotic Oscillator with Circulant Connection of Space Variables

Author

Nzoulewa Dountsop Sandrine and Kengne Jacques

Subjects
Electronic computers. Computer science, QA75.5-76.95
Abstract

In recent years, much energy has been devoted to the study of chaotic models with specific features particularly those with cyclic connection of the variables. Previous ones provide multistability, amplitude control, and so on. Concerning the first phenomenon, models with ring connection of variables presented a coexistence of up to twelve disconnected attractors. In order to emphasize the complexity of circulant chaotic oscillators and their use in the engineering domain, a quintic chaotic model with cyclic connection of variables is considered and studied, which has complex equilibria located on the line x=y=z=w. Therefore, it experiences, amongst other, the phenomenon of offset boosting obtained by introducing four constants into the equations of the model, which has not be done in the past. Multistability is also revealed and the coexistence of eight and sixteen attractors is demonstrated using phase portraits. The system’s dynamics has been investigated considering its two parameters. Nonlinear dynamical tools such as bifurcation diagrams, phase portraits, time evolutions, two-parameter diagram, and Lyapunov exponents help to highlight the important phenomena encountered. The numerical results are confirmed using PSpice and particularly show the double-band chaotic attractor. Moreover, total amplitude control (TAC) is shown, proving that our oscillator can be used as an attenuator or amplifier in the engineering domain. The method of adaptive synchronization has been applied to the considered oscillator to emphasize the possible implication into the secure of communication systems.

Published
2023
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