Chaotic resonance in biological neural networks

In nonlinear dynamic systems, the response to low amplitude signals can be optimized by the effect of some external stimuli. Among them, the intensity of noise generated by various environmental sources, in a certain range, increases the system response and this phenomenon is known as Stochastic Resonance. Furthermore, a similar enhancement effect can be achieved via a high frequency signal, instead of noise. This phenomenon is called Vibrational Resonance. On the other hand, in recent studies, it has been shown that these two phenomena can occur with the help of noise and high frequency signal in the nervous system, which is a nonlinear dynamic system, and besides there are other improving factors. One of these effects is chaotic activities. The response of a nonlinear system to a weak signal can be enhanced by the help of internal or external chaotic activity in the system and this is known as Chaotic Resonance. In this thesis, the effects of chaotic activity on the weak signal detection performance of Hodgkin-Huxley neurons are investigated in detail. For this purpose, the chaotic stimuli obtained by Lorenz, Chen and Chua systems, which are thought to mimic the chaotic behavior of the neuronal environment, are applied to a single isolated Hodgkin-Huxley neuron together with the weak signal. The obtained results have showed that Hodgkin-Huxley neuron exhibits chaotic resonance phenomenon depending on chaotic current density. It has been determined that there is an optimal chaotic current density which allows the Hodgkin-Huxley neuron to best detect the weak signal via chaotic resonance. In addition, the maximum Lyapunov exponent is used to determine whether the Hodgkin-Huxley neuron is in the chaotic regime or not. Accordingly, after determining the firing regime, it has been found that Hodgkin-Huxley neuron could detect weak signal even in chaotic regime. Investigating the presence of chaotic resonance in neuron populations, which has already been demonstrated to exist at a single neuron level, is of great importance for the integrity and inclusiveness of this phenomenon in the nervous system. The nervous system is quite complex in terms of the number of neurons and the connections between them that embody itself. The works in the field of computational neuroscience use network topologies modeled based on data obtained from neurophysiological imaging studies to investigate any phenomena observed in nature. In this context, in order to provide a wider perspective to the study, the effects of chaotic activity on the collective behavior of Hodgkin-Huxley neuron populations are investigated by using scale-free and small world networks that realistically reflect the connection structure of the brain at a very good level. According to the results, chaotic resonance is a robust phenomenon which can be observed in neuronal networks as well as at the level of single neuron. It has been observed that the chaotic resonance phenomenon that emerges in small world networks is not significantly affected by network parameters such as synaptic strength and connection density in performance. It has been seen that the optimal chaotic activity current density, which maximizes the signal processing performance of Hodgkin-Huxley neurons, is equal to the value required at the single neuron level. On the other hand, in scale-free networks, it has been found that the optimal chaotic activity current density, where weak signal processing performance is best, is increased to higher levels with increasing synaptic strength between neurons if the network has a sparse connectivity, i.e., smaller values of the average degree of connectivity. Furthermore, for the small values of the average degree of the network connection, it has also been shown that the amplitude values giving the maximum points of the chaotic resonances exhibit a bell-shaped resonance-like characteristic behavior as a function of synaptic strength. On the other hand, it has been observed that the neuronal system exhibits chaotic resonance for small values of synaptic strength between neurons at larger values of the average degree of the network, but resonance behavior disappears with increasing synaptic strength.