The effect of noise on strange nonchaotic attractors
نویسندگان
چکیده
The dynamical response of an underdamped Duffing oscillator to a quasiperiodic force is investigated in the presence and absence of very weak additive noise. Particular attention is focused on the effect of noise on the characteristics of strange nonchaotic attractors (SNAs). It is concluded that even extremely weak noise is sufficient to induce dynamical complexity in an SNA. PACS: 05.45.+b, 05.40.+j, 02.50.Ey keywords: strange nonchaotic attractor, noise in nonlinear system, Lyapunov exponent, dynamical and geometrical complexity.
منابع مشابه
Strange Nonchaotic Attractors in the Quasiperiodically forced Logistic Map
Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov exponent, as well as through the characteristic distributions of finite time Lyapunov exponents. Strange nonchaotic attractors can be created at a saddle–node bif...
متن کاملStrange nonchaotic attractors in random dynamical systems.
Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant...
متن کاملBlowout Bifurcation Route to Strange Nonchaotic Attractors.
Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. We show that for dynamical systems with an invariant subspace in which there is a quasiperiodic torus, the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic a...
متن کاملCharacterization of noise-induced strange nonchaotic attractors.
Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattractin...
متن کاملFractal properties of robust strange nonchaotic attractors in maps of two or more dimensions.
We consider the existence of robust strange nonchaotic attractors in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension D0 is larger than their information dimension D1 by 1 (i.e., D(0)=D(1)+1). We also show how this property is manifested in numerical experiments.
متن کامل