Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

In this paper, the extended Hindmarsh–Rose neuron model, which considers the slow intracellular exchange of calcium ions between its store and the cytoplasm, is studied. The dynamical behavior of this neuron model is analyzed by deriving the equilibrium points, the bifurcation diagrams, and the Lyapunov exponents, in the presence of an external forcing current. Furthermore, the dynamics of the network of the extended model is investigated. Firstly, a one-dimensional ring network is constructed, and the effects of the coupling strength and the forcing current are considered on the network behavior. The results confirm the existence of chimera state in small coupling strength values. Then, a square network of the proposed model is created by adding an external excitation to the neurons and four cases of different parameters are considered. Particularly, the effects of the stimulus parameters, the external current, and the coupling strength are studied on the emergence of spiral waves

Effects of partial time delays on synchronization patterns in Izhikevich neuronal networks

Abstract: Synchronization patterns have been observed in neuronal networks and are related to many cognitive functions and information processing and even some pathological brain states. In this paper, we study a ring network of non-locally coupled Izhikevich neurons with electrical synaptic coupling. Since it has been proved that time delays through gap junctions can simplify the synchronization, here we particularly investigate the effects of partial time delays on networks synchronization. By using two control parameters, the time delay and the probability of partial time delay, we show that partial time delays have a significant effect on the synchronization of this network. In particular, partial time delays can either increase or decrease the synchronization and also can induce synchronization transitions between coherent and incoherent states. Thus, partial time delays can cause chimera state, which is a special pattern when both synchronous and asynchronous states coexist and are strongly related to many real phenomena. Furthermore, partial time delays can change the period of synchronized neurons from period-1 to period-2 firing states that have different effects on information transmission in the brain. Graphical abstract: [Figure not available: see fulltext.]

Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

In this paper, the extended Hindmarsh–Rose neuron model, which considers the slow intracellular exchange of calcium ions between its store and the cytoplasm, is studied. The dynamical behavior of this neuron model is analyzed by deriving the equilibrium points, the bifurcation diagrams, and the Lyapunov exponents, in the presence of an external forcing current. Furthermore, the dynamics of the network of the extended model is investigated. Firstly, a one-dimensional ring network is constructed, and the effects of the coupling strength and the forcing current are considered on the network behavior. The results confirm the existence of chimera state in small coupling strength values. Then, a square network of the proposed model is created by adding an external excitation to the neurons and four cases of different parameters are considered. Particularly, the effects of the stimulus parameters, the external current, and the coupling strength are studied on the emergence of spiral waves

Birth and death of spiral waves in a network of Hindmarsh–Rose neurons with exponential magnetic flux and excitable media

Spiral waves are spatiotemporal patterns, observed in complex networks of biological oscillators such as heart and brain. In this paper, at first a modified Hindmarsh–Rose model with external electromagnetic radiation and discontinuous exponential flux coupling is introduced. Then a 2-dimensional network of the proposed model is constructed. The spatiotemporal patterns of the network are investigated in two different cases of periodic and quasi-periodic external magnetic excitations, by varying the external force parameters. As a consequence, the effective factors on the formation and elimination of spiral waves are reported.Scopu