混沌动力学
We discuss the behavior of the largest Lyapunov exponent $\lambda$ in the incoherent phase of large ensembles of heterogeneous, globally-coupled, phase oscillators. We show that the scaling with the system size $N$ depends on the details of…
Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional…
At low energies, the excitation of low frequency packets of normal modes in the Fermi-Pasta-Ulam (FPU) and in the Toda model leads to exponentially localized energy profiles which resemble staircases and are identified by a slope $\sigma$…
The Arnold Sommerfeld effect is an intriguing resonance capture and release series of events originally demonstrated in 1902. A single event is studied using a two degree of freedom mathematical model of a motor with imbalance mounted to…
The loss of synchronizability at large coupling strength is of major concern especially in the fields of secure communication and complex systems. Because theoretically, the coupling mode that can surely stabilize the chaotic/hyperchaotic…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation…
This paper presents a new generator of chaotic bit sequences with mixed-mode (continuous and discrete) inputs. The generator has an improved level of chaotic properties in comparison with the existing single source (input) digital chaotic…
The driven double-well Duffing oscillator is a well-studied system that manifests a wide variety of dynamics, from periodic behavior to chaos, and describing a diverse array of physical systems. It has been shown to be relevant in…
We discuss the effect of noise on a system with a quasi-periodicity of different dimensions. As the basic model of our research we use the simplest three-dimensional map with two-frequency and three-frequency quasi-periodicity. Modification…
A complex collective emerging behavior characterized by coexisting coherent and incoherent do- mains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators…
The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article we present two new…
We argue that a discrete Shilnikov attractor exists in the system of five identical globally coupled phase oscillators with biharmonic coupling. We explain the scenario that leads to birth of this kind of attractor and numerically…
We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have…
This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the…
The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the…
We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…
We establish the existence of `time quasicrystals', tilings of the time axis with two unit cells of different duration. These aperiodic tilings can be constructed as slices through regular tilings of a space spanned by two orthogonal time…
In the present paper the result of numerical simulations of the model based on the Hodgkin-Huxley formalism with bistability between hidden and rare attractors in the presence of noise are studied.
The chaotic behavior of the modified Rayleigh-Duffing oscillator with $ \phi^6$ potential and external excitation which modeles ship rolling motions are investigated both analytically and numerically. Melnikov method is applied and the…
Relay (or remote) synchronization between two not directly connected oscillators in a network is an important feature allowing distant coordination. In this work, we report a systematic study of this phenomenon in multiplex networks, where…