论文标题
一类分布式延迟微分方程的第二个解决方案
Period two solution for a class of distributed delay differential equations
论文作者
论文摘要
我们研究了具有分布式延迟的微分方程的周期性解决方案的存在。结果表明，对于一类分布式延迟差异的呼声，对称周期2解，该周期是最大延迟的两倍，作为普通微分方程的哈密顿量系统的周期性解决方案。该想法的证明基于（Kaplan＆Yorke，1974，J。Math。Anal。Appl。），用于具有奇数非线性函数的离散延迟微分方程。为了说明结果，我们提出了分布式延迟微分方程，这些方程具有根据jacobi椭圆函数表达的定期解决方案。
We study the existence of a periodic solution for a differential equation with distributed delay. It is shown that, for a class of distributed delay diferential quations, a symmetric period 2 solution, where the period is twice the maximum delay, is given as a periodic solution of a Hamiltonian system of ordinary differential equations. Proof of the idea is based on (Kaplan & Yorke, 1974, J. Math. Anal. Appl.) for a discrete delay differential equation with an odd nonlinear function. To illustrate the results, we present distributed delay differential equations that have periodic solutions expressed in terms of the Jacobi elliptic functions.
