On Periodic Solutions of Autonomous Systems

Journal Article · Thu Mar 15 04:00:00 EDT 2018 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/S10958-018-3681-8· OSTI ID:22771477

We propose a method for the investigation of periodic solutions of autonomous dynamical systems described by ordinary differential equations with phase and integral restrictions. We formulate the general problem of periodic solutions as a boundary-value problem with restrictions. By introducing a fictitious control, we transform the boundary-value problem into a control problem for dynamical systems with phase and integral restrictions. The control problem is solved by reducing it to an integral Fredholm equation of the first kind. We establish necessary and sufficient conditions for the existence of periodic solutions and propose an algorithm for finding periodic solution according to the limit points of the minimizing sequences.

• OSTI ID: 22771477
• Journal Information: Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 4 Vol. 229; ISSN JMTSEW; ISSN 1072-3374
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
DYNAMICAL SYSTEMS
FREDHOLM EQUATION
MATHEMATICAL SOLUTIONS
PERIODICITY