Chaotic Firings and Delayed Feedback Control of Rose-Hindmarsh Neuronal Model

Rose-Hindmarsh model is a simple and typical system for describing neuronal firing activities. This paper studies its chaotic firing phenomena, identification of unstable periodic orbits and chaos control in certain parameter regime. Firstly, irregular firing behaviors of the model are proved to be chaotic by numerically calculating the attractor's Lyapunov exponents and fractal dimension. Secondly, low order unstable periodic orbits embedded in the chaotic attractor are identified by simply analyzing interspike interval time series in their return maps. Finally, chaotic firings are stabilized to the period one and period two firing patterns respectively by delayed feedback control. Our preliminary work shows that the method of identification of unstable periodic orbits combined with delayed feedback control can effectively suppress irregular chaotic firings for the model. The technique presented in this paper is in accordance with those features of neuronal systems and may be a simple and actuated scheme for controlling chaotic firings of real neurons in physiological conditions.