Stability of autoresonance in dissipative systems

Abstract

Abstract. We consider a mathematical model describing the initial stage of a capture into autoresonance in nonlinear oscillating systems with a dissipation. Solutions whose amplitude increases unboundedly in time correspond to a resonance. An asymptotic expansion for such solutions is constructed as a power series with constant coefficients. The stability of autoresonance with respect to persistent perturbations is studied by means of Lapunov's second method. We describe the classes of perturbations for which a capture into autoresonance occurs.

Effect of Modulated Signals on Vibrational Resonance in a Harmonically Trapped Potential System

“…Further an increase of β, we can generate an odd number of potential wells. The equation for the root of the trapped potential system is (6) X * = 0 is always the root of the equation (6). Since the potential is symmetrical about x = 0, x * is also a root equation (6).…”

“…The equation for the root of the trapped potential system is (6) X * = 0 is always the root of the equation (6). Since the potential is symmetrical about x = 0, x * is also a root equation (6). It is not easy to find an analytical expression for x * from Eq.…”

“…Various types of resonance can be realized in nonlinear systems such as the stochastic resonance [1,2], coherence resonance [3,4], auto resonance [5,6], ghost resonance [7][8][9], chaos resonance [10,11], parametric resonance [12,13] and vibrational resonance [14][15][16][17][18]. The present paper is concerned with vibrational resonance.…”