论文标题
高阶Lohner-type算法，用于在延迟差分方程系统中严格计算庞加莱地图的严格计算
High-order Lohner-type algorithm for rigorous computation of Poincaré maps in systems of Delay Differential Equations with several delays
论文作者
论文摘要
我们提出了一种LOHNER型算法，用于具有多个延迟的延迟微分方程（DDE）系统的严格集成，并在计算PoincaréMaps中的应用来研究某些有界的，永恒的解决方案的动力学。该算法基于相位空间中溶液的分段泰勒表示，它利用了DDE中发生的溶液的平滑，以产生高阶溶液的外壳。我们应用拓扑技术来证明各种动力学行为，例如，在Mackey-Glass方程中存在（显然）（显然）不稳定的周期性轨道（在数值观察到混乱的参数方面）以及在被延迟效率磨损的chaotic Chaotic Ode（Rösssler系统）中的符号动力学的持久性。
We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincaré maps to study the dynamics of some bounded, eternal solutions. The algorithm is based on a piecewise Taylor representation of the solutions in the phase-space and it exploits the smoothing of solutions occurring in DDEs to produces enclosures of solutions of a high order. We apply the topological techniques to prove various kinds of dynamical behavior, for example, existence of (apparently) unstable periodic orbits in Mackey-Glass Equation (in the regime of parameters where chaos is numerically observed) and persistence of symbolic dynamics in a delay-perturbed chaotic ODE (the Rössler system).
