混沌动力学

Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces…

We demonstrate that the synergistic effect of a gauge field, Rashba spin-orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the…

The main aim of this paper is to detect dynamical properties of the Gy\"orgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations…

The mesochronic velocity is the average of the velocity field along trajectories generated by the same velocity field over a time interval of finite duration. In this paper we classify initial conditions of trajectories evolving in…

We generalize the two dimensional Lozi map in order to systematically obtain piece-wise continuous maps in three and higher dimensions. Similar to higher-dimensional generalizations of the related Henon map, these higher-dimensional Lozi…

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy or engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to…

In this paper, we show that "Labyrinth walks", the conservative version of "Labyrinth chaos" and member of the Thomas-R\"ossler class of systems, does not admit an autonomous Hamiltonian as a constant function in time, and as a consequence,…

Limit cycles (attractors for neighbouring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate "higher…

Intramolecular vibrational energy redistribution (IVR) impacts the dynamics of reactions in a profound way. Theoretical and experimental studies are increasingly indicating that accounting for the finite rate of energy flow is critical for…

This memoir is dedicated to the late Francis Hayin Ree, a formative influence shaping my work in statistical mechanics. Between 1963 and 1968 we collaborated on nine papers published in the Journal of Chemical Physics. Those dealt with the…

Due to the weak birefringence of single mode fibers, solitons generated in fiber lasers are indeed vector pulses and exhibit periodic parameter change including polarization evolution even when there is a polarizer inside the cavity. Period…

In the manifold theory of spiral structure in barred galaxies, the usual assumption is that the spirals rotate with the same pattern speed as the bar. Here we generalize the manifold theory under the assumption that the spirals rotate with…

The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the…

We use the one-dimensional Burgers equation to illustrate the effect of replacing the standard Laplacian dissipation term by a more general function of the Laplacian -- of which hyperviscosity is the best known example -- in equations of…

Transition from quasiperiodicity with many frequencies (i.e., a high-dimensional torus) to chaos is studied by using $N$-dimensional globally coupled circle maps. First, the existence of $N$-dimensional tori with $N\geq 2$ is confirmed…

In this article, we review the analytical and numerical approaches for computing the phase space structures in two degrees-of-freedom Hamiltonian systems that arise in chemical reactions. In particular, these phase space structures are the…

We propose a minimal coupled map lattice (CML) for the spiral pattern formation in astronomical objects which consist of accreting gas induced by gravity as a long-range force. In the proposed CML, we assume only two procedures: one in…

In the classical three rotor problem, three equal point masses move on a circle subject to attractive cosine potentials of strength g. In the center of mass frame, energy E is the only known conserved quantity. In earlier work [Krishnaswami…

One of the problems of periodic FPU-chains with alternating masses is whether significant interactions exist between the so-called (high frequency) optical and (low frequency) acoustical groups. We show that for $\alpha$-chains with $4n$…

Control and stabilization of irregular and unstable behavior of dynamic systems (including chaotic processes) are interdisciplinary problems of interest to a variety of scientific fields and applications. Using the control methods allows…