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2008•International Journal of Bifurcation and ChaosRequires access

TRANSITION TO CHAOS FROM QUASIPERIODIC MOTIONS ON A FOUR-DIMENSIONAL TORUS PERTURBED BY EXTERNAL NOISE

В. С. Анищенко, S. Nikolaev

Open publisher page 17 citations

Abstract

We propose a new autonomous dynamical system of dimension N = 4 that demonstrates the regime of stable two-frequency motions. It is shown that the system of two generators of quasiperiodic oscillations with symmetric coupling can realize motions on four-dimensional torus with resonant structures on it in the form of three- and two-dimensional torus. We show that with increase of noise intensity when the dimension of torus is higher it is destroyed faster.

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What this paper is about

We propose a new autonomous dynamical system of dimension N = 4 that demonstrates the regime of stable two-frequency motions. It is shown that the system of two generators of quasiperiodic oscillations with symmetric coupling can realize motions on four-dimensional torus with resonant structures on it in the form of three- and two-dimensional torus. We show that with increase of noise intensity when the dimension of torus is higher it is destroyed faster.

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OpenAlex reports 17 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We propose a new autonomous dynamical system of dimension N = 4 that demonstrates the regime of stable two-frequency motions. It is shown that the system of two generators of quasiperiodic oscillations with symmetric coupling can realize motions on four-dimensional torus with resonant structures on it in the form of three- and two-dimensional torus. We show that with increase of noise intensity when the dimension of torus is higher it is destroyed faster.

Key concepts: Quasiperiodic function, Torus, Noise (video), Physics, Dimension (graph theory), Coupling (piping), CHAOS (operating system), Classical mechanics

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TRANSITION TO CHAOS FROM QUASIPERIODIC MOTIONS ON A FOUR-DIMENSIONAL TORUS PERTURBED BY EXTERNAL NOISE — Research Paper | ScholarLens