We analyze the collective dynamics of an ensemble globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where splits into two internally synchronized clusters, as a consequence bistability individual oscillators. The multiplicity these solutions, induced by many possible ways distributing between implies that can exhibit multist...

In this paper, we study the following Duffing-type equation: x′′ + cx′ + g(t, x) = h(t), where g(t, x) is a 2π-periodic continuous function in t and concave-convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

Problem of unknown encoded parameter reconstruction is solved by means of procedure of design of adaptive observer for chaotic Duffing system. Unlike known analogues, the problem in question is only solved using measurements of output of chaotic system and in conditions of full parametrical uncertainty. Copyright © 2008 IFAC

A robust adaptation scheme for the delay of a continuous-time chaos control with half-period delayed feedback is presented. The phase-difference between the measured signal and the delayed measurement control is detected to adjust the delay to its optimum. The method when applied to the Lorenz and the Duffing oscillator shows high robustness. Copyright © 2002 IFAC

We study a type of p-Laplacian neutral Duffing functional differential equation with variable parameter to establish new results on the existence of T -periodic solutions. The proof is based on a famous continuation theorem for coincidence degree theory. Our research enriches the contents of neutral equations and generalizes known results. An example is given to illustrate the effectiveness of ...

This paper deals with the design of feedback controllers for a chaotic dynamical system l i e the Duffing equation. Lyapunov theory is used to show that the proposed bounded controllers achieve global convergence for any desired trajectory. Some simulation examples illustrate the presented ideas.

We investigate the dynamic quantum tunneling between two attractors of a mesoscopic driven Duffing oscillator. We find that, in addition to inducing a remarkable quantum shift of the bifurcation point, the mesoscopic nature also results in a perfect linear scaling behavior for the tunneling rate with the driving distance to the shifted bifurcation point.

Dynamic stabilization of an unstable periodic orbit, a new interesting non-equilibrium phenomenon in driven nonlinear systems, has been experimentally observed in an electronic analog circuit of a driven double-well Duffing oscillator. We suggest that the dynamic stabilization is a generic property of driven nonlinear systems with humped potentials. q 2000 Published by Elsevier Science B.V.