Self-Sustained Patterns On Neural Networks

Memory in animals has been investigated in various fields such as neuroscience, physics, mathematics, computer science, psychology etc. and has attracted much at-tention in interdiscipline. It has been revealed that the process of memory has three sequence stages:sensory memory, short-term memory and long-term memory. Many experiments have evidenced that memory with different time scales has different stages and is stored as self-sustained activity (also called persistent activity in neuroscience) in mammalian brains. The prerequisite is that recurrent excitatory loops within a neu-ral network can sustain a persistent activity recording from the physiological experi-ments.Self-sustained activity in neural systems has been studied basing on the tool of complex networks and computational neuroscience. We present an approach for con-trolling self-sustained activity oscillations by adding or removing one directed net-work link (a slight change) in coupled neural networks and also propose a simplified memory network model to show that self-sustained synchronous firing can be affected by heterogenous synaptic conductance in steady state,the topological parameters and external stimulus time. The model of Fitzhugh-Nagumo neurons coupled by dual-exponential chemical synapse has been investigated in neural systems. The character-istic feature of self-sustained oscillations is self-firing patterns.We study self-sustained oscillations by using phase plane analysis and the theory of Hopf-bifurcation with nu-merical simulation. The main results are concluded as follows:1、We present the third approach for generating self-sustained oscillations by changing network structure, in contrast to previous approaches of adding stimulus or noise. We find that the self-sustained patterns can be generated by adding one directed network link in both an isolated loop and a loop with 9 directed links based on synaptic conductance in the steady state. All the results show that a slight change (adding one new directed link) can produce self-sustained patterns.2、We also consider the case of removing a network link on the loop with 9 directed links. It is observed that the operation of adding and removing the link pe-riodically on different positions of the network induces two kinds of firing patterns, self-sustained firing pattern and on-off switch pattern, implying that the patterns can be controlled by only one link.3、We present a simplified memory network model to show that short-term mem-ory and long-term memory can be attained in coupling neural network. We find that the frequency of external stimulus can affect firing of two branches with different synap-tic conductances, i.e. cases of two constants (f= fr and f=fb) and heterogenous choice of f, in the simplified memory network. The two branches have the same den-sity of firing generating short-term memory when the frequency is not matched with two branches. The two branches cause the net firing forming long-term memory when the frequency is matched one of two branches.4、It is also found that the topological parameters influence the size of patterns and the external stimulus parameter determines the interval between two consecutive patterns in the simplified memory network. These findings suggest that the underling mechanism of short-term memory and long-term memory may be very simple.