We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and then undergoes a cascade of period-doubling route to chaos. We analytically derive the first Lyapunov coefficient to investigate the nature of Hopf bifurcation. We investigate well-separated regions for different kinds of attractors in the two-dimensional parameter space. Next, we introduce a timescale ratio parameter and calculate the slow manifold using geometric singular perturbation theory. Finally, the chaotic state annihilates by decreasing the value of the timescale ratio parameter.

中文翻译：

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另一个新的混沌系统：分岔与混沌控制

我们提出了一个具有两个非线性项的新的简单三维连续自主模型，并观察了系统参数的动态行为。该系统通过 Hopf 分岔改变了不动点的稳定性，然后经历了级联的倍周期路径到混沌。我们分析推导出第一个 Lyapunov 系数来研究 Hopf 分岔的性质。我们研究了二维参数空间中不同类型吸引子的良好分离区域。接下来，我们引入一个时间尺度比参数，并使用几何奇异微扰理论计算慢流形。最后，通过减小时间尺度比参数的值来消除混沌状态。