Elimination of spiral waves in a locally connected chaotic neural network by a dynamic phase space constraint.

In this study, a method is proposed that eliminates spiral waves in a locally connected chaotic neural network (CNN) under some simplified conditions, using a dynamic phase space constraint (DPSC) as a control method. In this method, a control signal is constructed from the feedback internal states of the neurons to detect phase singularities based on their amplitude reduction, before modulating a threshold value to truncate the refractory internal states of the neurons and terminate the spirals. Simulations showed that with appropriate parameter settings, the network was directed from a spiral wave state into either a plane wave (PW) state or a synchronized oscillation (SO) state, where the control vanished automatically and left the original CNN model unaltered. Each type of state had a characteristic oscillation frequency, where spiral wave states had the highest, and the intra-control dynamics was dominated by low-frequency components, thereby indicating slow adjustments to the state variables. In addition, the PW-inducing and SO-inducing control processes were distinct, where the former generally had longer durations but smaller average proportions of affected neurons in the network. Furthermore, variations in the control parameter allowed partial selectivity of the control results, which were accompanied by modulation of the control processes. The results of this study broaden the applicability of DPSC to chaos control and they may also facilitate the utilization of locally connected CNNs in memory retrieval and the exploration of traveling wave dynamics in biological neural networks.

Threshold control of chaotic neural network.

The chaotic neural network constructed with chaotic neurons exhibits rich dynamic behaviour with a nonperiodic associative memory. In the chaotic neural network, however, it is difficult to distinguish the stored patterns in the output patterns because of the chaotic state of the network. In order to apply the nonperiodic associative memory into information search, pattern recognition etc. it is necessary to control chaos in the chaotic neural network. We have studied the chaotic neural network with threshold activated coupling, which provides a controlled network with associative memory dynamics. The network converges to one of its stored patterns or/and reverse patterns which has the smallest Hamming distance from the initial state of the network. The range of the threshold applied to control the neurons in the network depends on the noise level in the initial pattern and decreases with the increase of noise. The chaos control in the chaotic neural network by threshold activated coupling at varying time interval provides controlled output patterns with different temporal periods which depend upon the control parameters.

Controlling chaos in a chaotic neural network.

The chaotic neural network constructed with chaotic neuron shows the associative memory function, but its memory searching process cannot be stabilized in a stored state because of the chaotic motion of the network. In this paper, a pinning control method focused on the chaotic neural network is proposed. The computer simulation proves that the chaos in the chaotic neural network can be controlled with this method and the states of the network can converge in one of its stored patterns if the control strength and the pinning density are chosen suitable. It is found that in general the threshold of the control strength of a controlled network is smaller at higher pinned density and the chaos of the chaotic neural network can be controlled more easily if the pinning control is added to the variant neurons between the initial pattern and the target pattern.