Stability of Impulsive Disturbance Complex-Valued Cohen-Grossberg Neural Networks in a Complex Number Domain
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摘要: 为了分析脉冲干扰因素对复数域神经网络的影响，研究了一类具有脉冲干扰的变时滞复数域Cohen-Grossberg神经网络的平衡点的动态行为.在假定放大函数、自反馈函数以及激活函数定义在复数域的情况下，首先，利用M矩阵和同胚映射的相关原理，分析了该系统平衡点的存在性和唯一性；其次，利用向量Lyapunov函数法以及数学归纳法，研究了该系统平衡点的全局模指数稳定性，并建立的稳定性判据；最后，通过两个数值仿真算例验证了所得结论的实用性和正确性.仿真结果显示系统状态在0.5 s便可收敛到平衡状态.研究结果表明：时滞和脉冲干扰强度越大、放大函数越小，则神经元状态的指数收敛速度越慢.
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关键词:
- Cohen-Grossberg神经网络 /
- 复数域 /
- 脉冲干扰 /
- 变时滞 /
- 模指数稳定性 /
- Lyapunov函数
Abstract: To analyse the effect of impulsive disturbances on neural networks, the dynamical behaviour of these disturbances was examined at the module of the equilibrium point of a class of complex-valued Cohen-Grossberg neural networks with time-varying delays. It was assumed that amplification, self-feedback, and activation functions were defined in a complex number domain. First, the existence and uniqueness of the equilibrium point of the system were analysed by utilising the corresponding property of the M matrix and the theorem of homeomorphism mapping. Second, the globally exponential stability of the module of the equilibrium point of the system was studied by applying the vector Lyapunov function and mathematical induction methods. The corresponding stability criteria were then established. Finally, two numerical examples from simulations were given to illustrate the practicability and correctness of the obtained results. The simulation results revealed that the states of the addressed system can reach equilibrium within 0.5 s. Other results showed that the greater the delay and impulsive strength and the smaller the amplification, the slower was the state convergence rate. -
图 1 情况1下无脉冲干扰时系统(22)状态的模曲线
Figure 1. Module curves of neuro states of Eq.(22) without impulsive disturbances under case 1
图 2 情况1脉冲干扰下系统(22)状态的模曲线
Figure 2. Module curves of neuro states of Eq.(22) with impulsive disturbances under case 1
图 3 情况2下无脉冲干扰时系统(22)状态的模曲线
Figure 3. Module curves of neuro states of Eq.(22) without impulsive disturbances under case 2
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