超混沌时滞动力系统同步的Langevin方法
Langevin approach to synchronization of hyperchaotic time-delay dynamics
摘要：
在本文中，我们描述了超混沌标量非线性延迟动力学的同步现象在一个充分发展的混沌制度。我们的研究结果依赖于这样的观察，在该制度下，一类超混沌吸引子的平稳统计特性可以用线性朗之万方程来再现，该方程定义为用三角洲相关噪声代替非线性延迟力。因此，同步现象可以用一组耦合的朗之万方程来解析表征。我们应用这种形式主义研究预期的同步动力学受到外部噪声波动，以及在超混沌通信方案的参数失配的影响进行表征。相同的过程被应用到与电光设备中的同步相关联的二阶微分延迟方程。在所有情况下，相对于完美同步的偏离通过相似性函数来测量。与超混沌动力学相关的离散映射的数值模拟支持该形式主义。
英文摘要：
In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical properties of a class of hyperchaotic attractors can be reproduced with a linear Langevin equation, defined by replacing the non-linear delay force by a delta-correlated noise. Therefore, the synchronization phenomenon can be analytically characterized by a set of coupled Langevin equations. We apply this formalism to study anticipated synchronization dynamics subject to external noise fluctuations as well as for characterizing the effects of parameter mismatch in a hyperchaotic communication scheme. The same procedure is applied to second order differential delay equations associated to synchronization in electro-optical devices. In all cases, the departure with respect to perfect synchronization is measured through a similarity function. Numerical simulations in discrete maps associated to the hyperchaotic dynamics support the formalism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
