Complex dynamics of a heterogeneous network of Hindmarsh-Rose neurons

Abstract

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.

Influence of the magnetic flux on the dynamics of a self-sustaining system: analytical, numerical and analogical investigations

“…The realization of electronic circuits is of great importance for laboratory experiments. We can mention the works of Hu et al [47,48], in which the analog circuit of the Morris-Lecar neuron model is provided to analyze the activity of neurons, the works of M.K.Wouapi et al [17,40,49] for the realization of the Fitzhugh-Nagumo model, the works of Matsumoto et al [50] on the bifurcations observed from electronic circuits, the works of Marins et al [51] on the simulations of a dynamical system model for electronic circuits, and some other works of Njitacke Tabekoueng et al [52][53][54][55][56][57]. Motivated by some results of the work, we realize in this section an analog electronic circuit of the neuron system coupled to magnetic flux.…”

Dynamics in a light-sensitive neuron with two capacitive variables

“…For example, photoelectric conversion in the visual neurons can turn help from the neural circuit coupled by photocells, and combination of two capacitors is helpful to discern the media difference between two sides of the cell membrane. When these reliable neuron models are clarified from physical viewpoint, cooperative behaviors is worthy of further investigation [67][68][69][70][71][72].…”

Mathematical generation of data-driven hippocampal CA1 pyramidal neurons and interneurons copies via A-GLIF models for large-scale networks covering the experimental variability range

“…[7,8,20,29] or adding noise to perturb morphological features in such a way to create copies whose firing patterns remains within experimental ranges (e.g. [10,22,25] and references therein). For accurate morphological and biophysical implementations (e.g.…”