Dynamic prediction modelling and equilibrium stability of a fractional discrete biophysical neuron model

Abstract

Here, we contemplate discrete-time fractional-order neural connectivity using the discrete nabla operator. Taking into account significant advances in the analysis of discrete fractional calculus, as well as the assertion that the complexities of discrete-time neural networks in fractional-order contexts have not yet been adequately reported. Considering a dynamic fast–slow FitzHugh–Rinzel (FHR) framework for elliptic eruptions with a fixed number of features and a consistent power flow to identify such behavioural traits. In an attempt to determine the effect of a biological neuron, the extension of this integer-order framework offers a variety of neurogenesis reactions (frequent spiking, swift diluting, erupting, blended vibrations, etc.). It is still unclear exactly how much the fractional-order complexities may alter the fring attributes of excitatory structures. We investigate how the implosion of the integer-order reaction varies with perturbation, with predictability and bifurcation interpretation dependent on the fractional-order β∈(0,1]. The memory kernel of the fractional-order interactions is responsible for this. Despite the fact that an initial impulse delay is present, the fractional-order FHR framework has a lower fring incidence than the integer-order approximation. We also look at the responses of associated FHR receptors that synchronize at distinctive fractional orders and have weak interfacial expertise. This fractional-order structure can be formed to exhibit a variety of neurocomputational functionalities, thanks to its intriguing transient properties, which strengthen the responsive neurogenesis structures.