Applied Problems of Nonlinear Oscillation and Wave Theory

In this paper the dynamics of two elastically coupled pendulums is studied. The pendulums oscillate under the influence of external rotational moments, their masses are considered to be equal. The current work is motivated by multiple applications in physics and biology that the model has.

The research is devoted to a method of diagnostics and quantitative analysis of chaotic synchronization in the presence of noise. We analyze how the additive white normal noise influences the accuracy of the measurement of synchronization of chaos. We also propose a new modification of the standard algorithm, which significantly reduces the sensitivity of the method to the noise.

The research is devoted to a method of diagnostics and quantitative analysis of chaotic synchronization in the presence of noise. We analyze how the additive white normal noise influences the accuracy of the measurement of synchronization of chaos. We also propose a new modification of the standard algorithm, which significantly reduces the sensitivity of the method to the noise.

In the article the description of dielectric constant of the structural elements of the chemical solution with the self-oscillating reaction Briggs–Rauscher, as measured reflection and transmission spectra of interacting with them the microwave radiation in the range of 5 to 8 GHz. It is shown that the solution may has properties of the photonic crystal with time-varying band gap.

The physical realizable system of ring structure, with a fixed irrational ratio of basic frequencies of external driving (the golden mean) manifests a strange nonchaotic attractor (SNA), similar to the attractor in the abstract map on a torus proposed and analyzed earlier by Hunt and Ott as an example of robust SNA.

A model of bistable stochastic oscillator with dynamical variables depending on dissipation is offered. Considered system demonstrates stochastic P-bifurcations and non-monotonic dependence of the mean oscillation frequency on the noise intensity. An effective noise intensity and an effective potential are introduced for a quantitative description of the observed effects.

We propose a modified method for computing of the largest Lyapunov exponent of chaotic oscillatory regimes from point processes at the presence of measurement noise that does not influence on the system’s dynamics. This modification allow a verification to be made of the estimated dynamical characteristics precision.

A method is proposed for generalized synchronization detection which does not exploit an auxiliary system. The method operates in a real time and uses a single response system that is driven alternately by the drive system signal and its delayed copy. A system of secure communication based on the proposed method is developed that has high resistance to noises of a transmission channel.