一类五维线性神经网络的复杂动力学行为研究
Research on the complex dynamical behavior for a 5-dimensional linear neural network
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摘要: 针对一类五维线性神经网络模型,通过引入一个保证系统一致有界的控制器,并研究该被控系统相空间体积元的变化率、Lyapunov指数,以及与耗散度之间的关系,得到系统状态的判断依据,即当参数不同时,系统分别为耗散混沌系统、保守系统和不稳定系统.仿真结果表明:改变系统参数值,系统随之呈现复杂动力学行为;系统参数满足一定条件时,被控系统进入超混沌状态.Abstract: Aiming at the model of a 5-dimensional linear neural network, a controller which could ensure that the solution of the controlled system was uniformly bounded was introduced to analyze the relationship between the change rate of the phase volume, Lyapunov exponents and the divergence of system.A judging standard for the controlled system was obtained, which meant that different system parameter would present different state, such as dissipative chaos system, conservative system and unstable system.Simulation results show that the system would present complex dynamical behaviors while the system parameters change, and the controlled system would be hyperchaotic when some conditions were satisfied.
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