Transient suppression of chaos in a Caputo fractional Rulkov neuron model induced by a single control impulse

Impulsive control of chaos in a fractional Rulkov neuron model is studied in this paper. Although control of fractional systems by a single impulse appears counterintuitive due to their long-term memory, it is shown that a properly chosen impulse can suppress chaotic firing. Naïve strategies based on placing the trajectory at the fixed point of the fractional map are ineffective. Instead, impulse magnitudes capable of suppression of chaos are identified using H-rank-based techniques. Depending on the impulse amplitude and timing, both permanent and transient suppression of chaos are observed. Permanent suppression occurs when the impulse transfers the system into the stable equilibrium, while transient suppression arises from the temporary stabilization of unstable equilibria. Delayed suppression of firing and spontaneous recovery of chaotic activity are also observed. These behaviors highlight the nontrivial role of memory effects in fractional dynamics. Although the system considered is a simple fractional Rulkov neuron model, the results suggest that fractional frameworks may offer important insight into transient neural control phenomena.