Controlling chaos in space-clamped FitzHugh–Nagumo neuron by adaptive passive method

The space-clamped FitzHugh–Nagumo (SCFHN) neuron exhibits complex chaotic firing when the amplitude of the external current falls into a certain area. To control the undesirable chaos in SCFHN neuron, a passive control law is presented in this paper, which transforms the chaotic SCFHN neuron into an equivalent passive system. It is proved that the equivalent system can be asymptotically stabilized at any desired fixed state, namely, chaos in SCFHN neuron can be controlled. Moreover, to eliminate the influence of undeterministic parameters, an adaptive law is introduced into the designed controller. Computer simulation results show that the proposed controller is very effective and robust against the uncertainty in systemic parameters.