Bistable systems of differential equations with time dependent voltage source E=E(t)

Abstract

This paper studies the asymptotic behavior of solutions of bistable system with time dependent voltage source E=E(t). Under the assumption that either E(t)−E_o is absolutely integrable on [0 ∞) for some constant E_o or E(t) is nondecreasing, several convergence criteria for solutions of bistable systems are given. These results guarantee that every solution of such a system converges to the equilibria of its limiting equations and generalize all results of Moser[l] and some results in [2]. For the single diode circuit whose characteristic function is a polynomial of degree 3, the chaotic behavior of the system is investigated and the condition for the existence of Smale horseshoe is provided.

Keywords:

• Bistable system
• asymptotic convergence
• Smale horseshoe
• La Salle invariance principle
• Melnikov's method

AMS:

• 34C11
• 58F13
• 94C99