Effects of autapse on inverse chaoti̇c resonance i̇n the Morris Lecar neuron model

Neurons are the fundamental building blocks of our nervous system and are critical for understanding brain functions and treating diseases. Computational neuroscience provides mathematical models for disciplines such as neural networks, biologically examined neurons,their physiology and dynamics, psychological connections, and learning mechanisms of living organisms. This thesis examines the effects of electrical, excitatory and inhibitory autapses on the firing behaviour of the Morris-Lecar (ML) neuron in the presence of chaotic activity. The study analyses the effects of autaptic conductance and autaptic time delay parameters on the mean firing rate (MFR) of the ML neuron under different chaotic current intensities. The obtained findings indicate that in the absence of autapse, low chaotic current intensity leads to regular firing, medium intensity completely suppresses firing and high intensity results in intermittent firing and quiescence, providing evidence for the phenomenon of inverse chaotic resonance.The effects of electrical autapse on MFR have been analyzed. Obtained results shows that at low chaotic signal intensity, the autapse can increase or decrease MFR or completely silence the neuron; at medium intensity, the neuron transit between quiescence and firing states, exhibiting a multi-ICR phenomenon; and at high intensity, the neuron maintains a minimum firing frequency of 5 Hz. Additionally, the effects of inhibitory autapse on inverse chaotic resonance have been examined. At low chaotic current intensity, the impact of the autapse on MFR is minimal at low τ values. However, as τ increases and within specific κ values, the neuron shows firing-quiescence patterns, indicating a multi-ICR phenomenon. When the ML neuron is considered to have an excitatory autapse, at medium chaotic current intensity, the neuron is completely quiescent at low κ values, while showing quiescence-firing patterns at medium κ ranges. At high chaotic current intensity, the firing frequency of the neuron varies between 5.18-11 Hz, but complete quiescence does not occur. Regardless of the type of autapse, it can switch the Morris-Lecar neuron from firing to quiescence and from quiescence to firing, and under specific parameter values, it can trigger multiple inverse chaotic resonances.