Periodic Solutions of Delay-Differential Equations with a Restorative Condition
نویسنده
چکیده
A global existence theorem is given for the periodic solutions of a class of scalar delay-differential equations satisfying a restorative condition. Properties concerning the period and the amplitude of the slowly oscillating periodic solutions are established. The results are applied to a physiological reflex model exhibiting asymmetry of response. It is shown that the model predicts periodic behavior for sufficiently large values of the delay. Furthermore, the two sources of nonlinearity in the model are shown to be responsible for different aspects of dynamics: The presence of the response asymmetry affects the local dynamics in the vicinity of an equilibrium, while the global behavior is mostly determined by the feedback in the reflex path.
منابع مشابه
Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay
...
متن کاملEXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY
متن کامل
Periodicity in a System of Differential Equations with Finite Delay
The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.
متن کاملPeriodic solutions of fourth-order delay differential equation
In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$ is investigated. Some new positive periodic criteria are given.
متن کاملA Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations with Distributed Delay
A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.
متن کامل