Related papers: Randomness, chaos, and structure
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
We study raw coding of trajectories of a chaotic dynamical system by sequences of elements from a finite alphabet and show that there is a fundamental constraint on differences between codes corresponding to different trajectories of the…
In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions. In this study, a quantitative method…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach for detecting of synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different…
Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
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…
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…
Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime. The challenge is even greater when the physics underlying such systems is…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
We present a methodology to characterize synchronization in time series based on symbolic representations. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to…
In this paper, the familiar problems of free-fall motion and simple harmonic motion (SHM) are combined. The novel composite system passes from regular to chaotic behavior for increasing values of energy $E$. This system is a suitable…