Related papers: Chaotic behavior of the $P$-adic Potts-Bethe mappi…
The letter proposes a procedure for generation and control chaotic beats in a dynamical system being initially in the periodic state. The dynamical system describes a simple nonlinear optical process -- second-harmonic generation of light.…
With a view to understanding the ``rheochaos'' observed in recent experiments in a variety of orientable fluids, we study numerically the equations of motion of the spatiotemporal evolution of the traceless symmetric order parameter of a…
A $p$-local compact group is an algebraic object modelled on the homotopy theory associated with $p$-completed classifying spaces of compact Lie groups and p-compact groups. In particular $p$-local compact groups give a unified framework in…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval. We investigate the possibility of having power-law tails in the invariant measure by approximate solution of the…
Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously…
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…
In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…
An important aspect of the physics of amorphous solids is the onset of irreversible behavior usually associated with yield. Here we study amorphous solids under periodic shear using quasi-static molecular dynamics simulations and observe a…
Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent…
We demonstrate chaotic behavior of timelike, null and spacelike geodesics in non-homogeneous vacuum pp-wave solutions. This seems to be the first known example of a chaotic motion in exact radiative spacetime.
Chaotic dependence on temperature refers to the phenomenon of divergence of Gibbs measures as the temperature approaches a certain value. Models with chaotic behaviour near zero temperature have multiple ground states, none of which are…
We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary wave collisions depends on the transfer of energy to…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
In this work we study possibility of chaos formation in the dynamics governed by paradigmatic model of Cavity Quantum Electrodynamics, the so called James-Cammings model. In particular we consider generalized JC model. It is shown that even…
By a classical result of Kathleen Alligood and James Yorke we know that as we isotopically deform a map $f:ABCD\to\mathbb{R}^2$ to a Smale horseshoe map we should often expect the dynamical complexity to increase via a period--doubling…
Using $p$-adic numbers, we partially categorize the cycles of a sizable class of polynomial dynamical systems. In turn, we prove a few results related to the non-trivial cycles of the $\textit{Collatz map}$ $\text{Col} : \mathbb{Z}_+ \to…
Let $f$ be a non-constant complex-valued analytic function defined on a connected, open set containing the $L^p$-spectrum of the Laplacian $\mathcal L$ on a homogeneous tree. In this paper we give a necessary and sufficient condition for…
We study numerically chaotic behavior associated with a hyperbolic strange attractor of Plykin type in the model of Hunt, an artificially constructed dynamical system with continuous time. There are presented portraits of the attractor,…
Restarting a stochastic search process can accelerate its completion by providing an opportunity to take a more favorable path with each reset. This strategy, known as stochastic resetting, is well studied in random processes. Here, we…
In this paper for the Potts-SOS model on a Cayley tree under some conditions the existence of at least one periodic (non translation-invariant) Gibbs measure is proved.