Study Of Multi-frequency Sinusoidal Wave Control In A Chaotic Neural Network

Chaotic neural networks(CNNs), which were proposed on the basis of abundant chaotic dynamics in biology neural systems, have rich dynamics and potential application in information processing such as memory search and pattern recognition. However, the chaotic characteristic makes its outputs unstable, which imped its direct applications in information processing. Therefore, chaotic control in CNNs has been a hot research topic in the research field of CNNs.Up to now, most of chaos control methods of CNNs were proposed on the basis of mathematical considerations, and the phenomena of the real brain are not taken into account. Zhang et al proposed sinusoidal modulation control method in which a sinusoidal wave reflecting the characteristic of brain waves is used as a control signal to modulate the refractory scaling parameter in Aihara CNN. Chaos in the CNN can be controlled by using the method. Since the brain waves in cerebral neural systems are not single frequency sinusoidal, in this thesis we propose control methods which use multiple frequency sinusoidal waves to modulate the refractory scaling parameter of the CNN, and perform systematic simulation experiments.We propose two control ways:1. two sinusoidal wave signals are added to different parts of chaotic neurons respectively.2. A control signal with a mixture of two different frequency sinusoidal waves is added to all chaotic neurons. Research shows that the value of the frequency parameters of the control signals is critical for the control effect. When the frequencies of the control signals fall in the bands of the brain waves of working or thinking activities, both control methods can control the chaos in the CNN, and the controlled CNN converges in a periodic orbit which only contains the store pattern and its reverse pattern related to the initial pattern of the network. In addition, the control effect depends on the initial phases of both sinusoidal waves when a control signal with a mixture of two different frequency sinusoidal waves.Our work supports Freeman’s supposition that self-induced chaos control in the brain might play a key role in recognition and learning processing in biology neural systems. Moreover, it is helpful for us to understand the conscious activity.