混沌动力学
Let $f,g$ be affine circle maps and let $[f,g]$ be the alternating system generated by $f$ and $g$. We present an algorithm to compute the periodic structure of $[f,g]$.
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…
We present a global analysis of the center manifold of the collinear points in the circular restricted three-body problem. The phase-space structure is provided by a family of resonant 2-DOF Hamiltonian normal forms. The near 1:1…
In this work, we investigate resonance and antiresonance behaviour in forced coupled Duffing oscillators with nonlinear damping. Further, we will analyse the parameter dependence of the frequency response and stability. In the course of all…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial…
Chaotic dynamics is an important source for generating pseudorandom binary sequences (PRNS). Much efforts have been devoted to obtaining period distribution of the generalized discrete Arnold's Cat map in various domains using all kinds of…
We investigate the dynamics of a delay differential coupled Duffing-Van der Pol oscillator equation. Using the Lindstedt's method, we derive the in-phase mode solutions and then obtain the slow flow equations governing the stability of the…
Aspects of the Nos\'e and Nos\'e-Hoover dynamics developed in 1983-1984 along with Dettmann's closely related dynamics of 1996, are considered. We emphasize paradoxes associated with Liouville's Theorem. Our account is pedagogical, focused…
A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely…
Advection-diffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent…
It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic…
We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Li\'enard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
This note studies 1 and 2 degree of freedom hamiltonian systems that are thermostated by a single-variable thermostat. Under certain conditions on the hamiltonian and thermostat, the existence of a horseshoe in the flow of the thermostated…
We generalize the concept of randomness in an infinite binary sequence in order to characterize the degree of randomness by a real number D>0. Chaitin's halting probability \Omega is generalized to \Omega^D whose degree of randomness is…
We discuss two mechanical systems with hyperbolic chaotic attractors of Smale - Williams type. Both models are based on Froude pendulums. The first system is composed of two coupled Froude pendulums with alternating periodic braking. The…
The article considers Chaplygin sleigh on a plane in potential well, assuming that an external potential force is supplied at the mass center. Two particular cases are studied in some detail, namely, a one-dimensional potential valley and a…
Extreme events are characterised by low probabilities and high impact on the systems. As a consequence, it is possible to find many studies about the predictability and suppression of extreme events. In this work, we show the existence of…
Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations…