混沌动力学
Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…
Understanding the topological structure of phase space for dynamical systems in higher dimensions is critical for numerous applications, including the computation of chemical reaction rates and transport of objects in the solar system. Many…
This work presents the continuation of the recent article "The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension", published in the Nonlinear Dynamics journal. In this work, in comparison with the results for…
An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are…
Dynamics of nonlinear coupled driven oscillators is investigated. Recently, we have demonstrated that the amplitude profiles -- dependence of the amplitude $A$ on frequency $\Omega$ of the driving force, computed by asymptotic methods in…
Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces…
In this work, we report the emergence of extreme events in a damped and driven velocity-dependent mechanical system. We observe that the extreme events emerge at multiple points. We further notice that the extreme events occur symmetrically…
We review the geometric structure of the IL$^0$PE model, a rotating shallow-water model with variable buoyancy, thus sometimes called ``thermal'' shallow-water model. We start by discussing the Euler--Poincar\'e equations for rigid body…
Resonances in particle transmission through a 1D finite lattice are studied in the presence of a finite number of impurities. Although this is a one-dimensional system that is classically integrable and has no chaos, studying the…
This paper deals with the derivation and analysis of a seventh-order generalization of the H\'enon-Heiles potential. The new potential has axial and reflection symmetries, and finite escape energy with three channels of escape. Based on…
We analyse the infinite-dimensional limit of the maximally chaotic dynamical systems that are defined on N-dimensional tori. These hyperbolic systems found successful application in computer algorithms that generate high-quality…
This short paper addresses quasi synchronization of heterogeneous complex dynamical networks. The similarity and difference between synchronization of homogeneous systems and quasi synchronization of heterogeneous complex dynamical networks…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
Various dynamical engineering systems involve purely nonlinear stiffness that lacks linear properties even under the assumption of small displacements. The most common is the cubic nonlinearity that may stem from either geometric or…
The amplitude-dependent frequency of the oscillations, termed \emph{nonisochronicity}, is one of the essential characteristics of nonlinear oscillators. In this paper, the dynamics of the Rossler oscillator in the presence of…
We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…