Related papers: A New Test for Chaos

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.…

We formulate the conditions under which the dynamics of a continuously measured quantum system becomes indistinguishable from that of the corresponding classical system. In particular, we demonstrate that even in a classically chaotic…

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…

We adopt the '0-1' test for chaos using Brownian motion chains to identify the dynamics of the Ricker's population model. In the '0-1' test '0' is related to regular motion while '1' is associated with chaotic motion. The identified regular…

This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…

Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from…

One of the major breakthroughs in science of the last (20th) century was building a bridge between the worlds of stochastic (random) systems and deterministic (dynamical) systems. It was started by the celebrated 1958 paper by…

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…

Violent relaxation (VR) is often regarded as the mechanism leading stellar systems to collisionless meta equilibrium via rapid changes in the collective potential. We investigate the role of chaotic instabilities on single particle orbits…

Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…

We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting and neutral manifolds of…

A new dynamical parameter, the f-indicator, is introduced and used in order to distinguish between regular and chaotic motion in galactic Hamiltonian systems. Two kinds of galactic potentials are used: (i) a global potential, which…

Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…

Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention…

We observe chaotic dynamics in a damped linear oscillator, which is driven only at certain regions of phase space. Both deterministic and random drives are studied. The dynamics is characterized using standard techniques of nonlinear…

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…

We consider non-i.i.d. random holomorphic dynamical systems whose choice of maps depends on Markovian rules. We show that generically, such a system is mean stable or chaotic with full Julia set. If a system is mean stable, then the…

In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the…

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…

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…