相关论文: At the very origin of chaos in three-dimensional d…

A 3D dynamical model with a quasi-homogeneous core and a disk component is used for the chaos control in the central parts of elliptical galaxy. Numerical experiments in the 2D system show a very complicated phase plane with a large chaotic…

A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary…

Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…

Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic…

We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be…

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period…

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in…

Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…

In this paper the chaotic properties of the TCP congestion avoidance mechanism are investigated. The analysis focuses on the origin of the complex behavior appearing in deterministic TCP/IP networks. From the traffic modeling point of view…

This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic…

In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…

A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…

A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…

When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…

Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1-$d$ map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic…

We consider classical two-dimensional Kepler system with spin-orbit coupling and show that at a sufficiently strong coupling it demonstrates a chaotic behavior. The chaos emerges since the spin-orbit coupling reduces the number of the…

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…

The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…