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A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
In this work, we demonstrate the open-loop control of chaotic systems by means of optimized periodic signals. The use of such signals enables us to reduce control power significantly in comparison to simple harmonic perturbations. It is…
We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…
It is known that the set of all nonnegative integers may be equipped with a total order that is chaotic in the sense that there is no monotone three-term arithmetic progressions. Such chaotic order must be so complicated that the resulting…
The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…
We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple…
We predict theoretically and verify experimentally the suppression of chaos in the Lorenz system driven by a high-frequency periodic or stochastic parametric force. We derive the theoretical criteria for chaos suppression and verify that…
Quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. {\bf 57}, 30 (1929)] and again by Reimann [Phys. Rev. Lett. {\bf 101}, 190403 (2008)] in a more practical and well-defined form. However, it…
The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observational data. Yet the reliability of learned surrogates and…
By folding nonautonomous differential systems in the plane to scalar differential equations, a sufficient condition for the non-occurrence of chaotic behavior is obtained.
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
We show that stability of planetary systems is intimately connected with their internal order. An arbitrary initial distribution of planets is susceptible to catastrophic events in which planets either collide or are ejected from the…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
Since Kopel's duopoly model was proposed about three decades ago, there are almost no analytical results on the equilibria and their stability in the asymmetric case. The first objective of our study is to fill this gap. This paper analyzes…
Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…