一个简单延迟非线性系统的动力学行为及混沌同步

分析一个简单二阶延迟系统的Hopf分支和混沌特性, 包括分支点、分支方向和分支周期解的稳定性, 解析求出退延迟情况下, 这个系统的相轨线方程; 通过数值计算并绘制分岔图, 揭示系统存在由倍周期通向混沌的道路; 利用单路线性组合信号, 反馈控制实现系统的部分完全同步; 利用主动-被动与线性反馈的联合, 实现系统的完全同步; 设计和搭建系统的电子实验线路, 并从实验中观测到与理论分析或数值计算相一致的结果. 关键词： 延迟非线性系统 电路实验 Hopf分支 混沌

Dynamic behavior and chaos synchronization of a simple nonlinear time-delayed system

Hopf bifurcation and chaotic properties of a simple second order time-delayed system, which includes bifrucation point, bifurcation direction and the stability of bifrucating periodic solutions, are analyzed. We obtain analytically the phase trajectory equations when the delay degenerates. Furthermore, through bifurcation diagram drawn by means of numerical simulation, the route from period-doubling bifurcation to chaos is reaveled; using single linearly combinating signals and the feedback control method, we achieve partial synchronization of the system. Combining the active-passive method with the linear feedback method, we have realized complete synchronization. In addition, we have designed and built an electronic experimental line, from which the same result as the theoretical analysis or numerical results are obtained.
Keywords： nonlinear time-delayed system electronic circuits Hopf bifurcation chaos