A unified control theorem is presented in this paper, whose aim is to suppress the transversal intersections of stable and unstable manifolds of homoclinic and heteroclinic orbits in the Poincarè map embedding in system dynamics.
In particular, a variety of homoclinic trajectories connected with two Lyapunov orbits are detected.
Hence, problem (4.1) has an unbounded sequence of homoclinic solutions.
Then problem (1.1) has an unbounded sequence of homoclinic solutions.
Hence, system (1.1) possesses an unbounded sequence of homoclinic solutions.
For more problems of homoclinic solutions, see [5 8].
This paper describes the use of this polyhedral representation for the detection of homoclinic and heteroclinic connections.
More precisely, many authors studied the existence and multiplicity of homoclinic solutions for (HS); see [5 17].
The following properties of damped and escape solutions are important for the existence of homoclinic solutions.
The problem of swinging up inverted pendulums has often been solved by stabilizing a particular class of homoclinic structures present in the dynamics of a physical pendulum.
