Adaptive resonance and control of chaos in a new memristive generalized FitzHugh-Nagumo bursting model

In a new memristive generalized FitzHugh-Nagumo bursting model, adaptive resonance (AR), in which the neuron system's response to a varied stimulus can be improved by the ideal intensity of adaptation currents, is examined. We discovered that, in the absence of electromagnetic induction, there is signal detection at the greatest resonance peak of AR using the harmonic balance approach. For electromagnetic induction's minor impacts, this peak of the AR is optimized, whereas for its larger effects, it disappears. We demonstrate dependency on adaption strength as a bifurcation parameter, the presence of period-doubling, and chaotic motion regulated and even annihilated by the increase in electromagnetic induction using bifurcation diagrams and Lyapunov exponents at specific resonance frequencies. The suggested system shows the propagation of localized excitations as chaotic or periodic modulated wave packets that resemble breathing structures. By using a quantitative recurrence-based analysis, it is possible to examine these plausible dynamics in the structures of the recurrence plot beyond the time series and phase portraits. Analytical and numerical analyses are qualitatively consistent.