Noise induced suppression of spiral waves in a hybrid FitzHugh–Nagumo neuron with discontinuous resetting

Abstract

A modified FitzHugh-Nagumo neuron model with sigmoid function-based recovery variable is considered with electromagnetic flux coupling. The dynamical properties of the proposed neuron model are investigated and as the excitation current becomes larger, the number of fixed points decreases to one. The bifurcation plots are investigated to show the chaotic and periodic regimes for various values of excitation current and parameters. A network of the neuron model is constructed to study the wave propagation and wave re-entry phenomenon. Investigations are conducted to show that for larger flux coupling values, the spiral waves are suppressed but for such values of the flux coupling the individual nodes are driven into periodic regimes. By introducing Gaussian noise as an additional current term we showed that when noise is introduced for entire simulation time, the dynamics of the nodes are largely altered while the noise exposure for 200-time units will not alter the dynamics of the nodes completely. Keyboards: FitzHugh-Nagumo neuron; hybrid neuron; resetting; spiral waves; noise effectsFitzHugh-Nagumo neuron models are simplest yet one of the effective mathematical models used to define the bursting and spiking phenomenon of neurons. We modified the model by including sigmoid based recovery variable and flux coupling. Dynamical behaviours and properties of the modified model is investigated. A network model of the neuron model is constructed, and wave propagation phenomenon is studied. We could effectively show the emergence of spiral waves in the network and by including the noise effects we could show that introducing noise can suppress spiral waves.

Local and Network Dynamics of a Non-Integer Order Resistor–Capacitor Shunted Josephson Junction Oscillators

“…In the following, we looked at the influence of BM noise [51,52] on observed SW in the array of FJJ by distributing it in two distinct ways. Firstly, the behavior of the network is analyzed by distribution noise throughout the simulation time.…”

“…Furthermore, noise is ubiquitous and can inevitably exist in many practical systems [51,52]; a wide range of studies have been conducted in the literature to explore the impacts of noise in dynamical systems. In particular, state-dependent noise is used to suppress chaos in fractional order chaotic systems [53].…”

Enhance sensitivity to illumination and synchronization in light-dependent neurons*

“…From dynamical viewpoint, numerical approach can be used to detect the suitable coupling intensity for stabilizing complete synchronization via bifurcation analysis, calculating the Lyapunov exponents and using saturation gain method. [56] Indeed, the application of master stability function [57][58][59][60] provides helpful guidance to discern the possibility of synchronization control in dynamical systems. In fact, it is more worth investigating the collective behaviors and synchronization stability in memristive neural networks [61][62][63][64] considering the effect of time delay and parameter perturbations by applying feasible schemes.…”

Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network

“…In addition, it is found that there are very complex dynamic phenomena in the FHN model. Rajagopal et al (10) studied chaos and periodic bifurcation diagrams under different excitation currents and found that the dynamic behavior of the nodes alters dramatically after the introduction of Gaussian noise.…”

“…In addition, it is found that there are very complex dynamic phenomena in the FHN model. Rajagopal et al ( 10 ) studied chaos and periodic bifurcation diagrams under different excitation currents and found that the dynamic behavior of the nodes alters dramatically after the introduction of Gaussian noise. Iqbal et al ( 11 ) studied robust adaptive synchronization of a ring-coupled uncertain chaotic FHN model and proposed a scheme to synchronize the coupled neurons under external electrical stimulation.…”