Chaotic phenomena may exist in nonlinear evolution equations. In many cases, they are undesirable but can be controlled. In this study, we deal with the chaos control of a three-dimensional chaotic system, reduced from a KdV–Burgers–Kuramoto equation. By adding a single delay feedback term into the chaotic system, we investigate the local stability and occurrence of Hopf bifurcation near the equilibrium point. Some dynamical properties including the direction and stability of bifurcated periodic solutions are presented by using the normal form theory and the center manifold theorem. Numerical simulations are illustrated which agree well with the theoretical results.

中文翻译：

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具有延迟反馈的 KdV-Burgers-Kuramoto 系统的 Hopf 分岔

非线性演化方程中可能存在混沌现象。在许多情况下，它们是不可取的，但可以控制。在这项研究中，我们处理从 KdV-Burgers-Kuramoto 方程简化的三维混沌系统的混沌控制。通过在混沌系统中添加单个延迟反馈项，我们研究了平衡点附近的局部稳定性和 Hopf 分岔的发生。利用范式理论和中心流形定理，给出了分叉周期解的方向性和稳定性等动力学性质。数值模拟与理论结果吻合得很好。