Josephson环耦合量子细胞神经网络混沌动力学分析

Chaotic Dynamical Analysis of Josephson-Circuit-Coupled Quantum Cellular Neural Network

量子细胞神经网络(QCNN)在大规模信号处理上是一种崭新的结构,将是未来细胞神经网络(CNN)一个新的发展方向。以Josephson环的幅值和相位作为状态变量,研究了两个Josephson环耦合的量子细胞神经网络的非线性动力学行为。通过理论研究和计算机仿真,发现系统具有丰富的动力学行为,如周期、拟周期、混沌和超混沌状态。分析了细胞内隧穿矩阵元比例系数和相邻细胞互感系数对系统分岔与混沌特性的影响,发现系统经拟周期分岔进入混沌,在不对称细胞耦合的量子细胞神经网络中,系统能产生混沌的参数范围较大,且在混沌区域没有周期窗口,是一种鲁棒混沌;在对称细胞耦合的量子细胞神经网络中,系统能产生混沌的的参数范围相对较小,且在产生混沌振荡的区域内有周期、拟周期窗口。

Quantum cellular neural network（QCNN）is an innovative architecture for the massive signal processing,and will be a new development direction of the cellular neural network（CNN）in the future.With the amplitude and phase of the Josephson circuit as state variables,the nonlinear dynamical behavior of two Josephson-circuit-coupled QCNN was studied.Through theoretical analysis and computer simulation,it is found that the system has abundant dynamic behavior,such as periodic,quasi-period,chaotic and hyper-chaotic states.The influences of the intra-cell tunneling matrix element and mutual inductance of adjacent cells on the system bifurcation and chaotic behavior were analyzed.It is found that the system enters into the chaotic state from quasi-periodic state by the quasi-period bifurcation,and in the unbalanced cell coupled QCNN,the parameter range of the system to produce chaotic oscillation is large,and the system has no period windows in the chaos region,the chaos in the QCNN is robust.In the balanced cell coupled QCNN,the parameter range of the system to produce chaotic oscillation is relative small,the system has the period and quasi-period windows in chaos region.