Related papers: Nonlinear Physics: Integrability, Chaos and Beyond
Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer- assisted computations. As an…
The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the…
A central paradigm of non-equilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex…
We reconsider the persistence of information under the dynamics of the logistic map in order to discuss communication through a nonlinear channel where the sender can set the initial state of the system with finite resolution, and the…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
In previous study [1], we proposed a new physical law applicable to both particle and thermodynamical systems. Additionally, we introduced a physical definition of chaos and self-organization. In the present work, we extend this novel…
Dynamics of two anharmonic oscillators with interaction of the fourth order has been investigated. The conditions at realization of which system is integrable are established. The exact analytical solution of the nonlinear equations in the…
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…
The macroscopic zero-temperature behavior of weakly- incommensurate systems in one dimension is described in terms of solitons. The soliton density n obeys equations displaying several types of singular interface-like solutions: (i)…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…
We describe some highlights in the theory of chaos, that started with Poincare (1899). Generic systems have both ordered and chaotic domains. Chaos appears mainly near un- stable periodic orbits. Large chaotic domains are due to resonance…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Regular and chaotic test particle motion in gravitational fields due to stellar bodies with quadrupolar and octupolar deformation are studied using Poincare surfaces of section. In first instance, we analyze the purely Newtonian case and we…
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability,…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Conventional artificial neural networks are powerful tools in science and industry, but they can fail when applied to nonlinear systems where order and chaos coexist. We use neural networks that incorporate the structures and symmetries of…
Integrable quantum systems of finite size are generically robust against weak enough integrability-breaking perturbations, but become quantum chaotic and thermalizing if the integrability-breaking is strong enough. We argue that the onset…
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…