Related papers: Can two chaotic systems give rise to order?
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
Inspired by the flashing ratchet, Parrondo's game presents an apparently paradoxical situation. Parrondo's game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
Chaotic systems can be synchronized by linking them to a common signal, subject to certain conditions. However, the presence of multiple driving signals coming from different systems, give rise to novel behavior. The particular case of…
We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic…
A novel type of self-organized lattice in which chaotic defects are arranged periodically is reported for a coupled map model of open flow. We find that temporally chaotic defects are followed by spatial relaxation to an almost periodic…
Two chaotic systems which interact by mutually exchanging a signal built from their delayed internal variables, can synchronize. A third unit may be able to record and to manipulate the exchanged signal. Can the third unit synchronize to…
The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
In the 60's Shapley provided an example of a two player fictitious game with periodic behaviour. In this game, player $A$ aims to copy $B$'s behaviour and player $B$ aims to play one ahead of player $A$. In this paper we continue to study a…
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped…
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
We construct a Parrondo's game using discrete time quantum walks. Two lossing games are represented by two different coin operators. By mixing the two coin operators $U_{A}(\alpha_{A},\beta_{A},\gamma_{A})$ and…
Dormancy is a costly adaptive strategy that is widespread among living organisms inhabiting diverse environments. We explore mathematical models of predator-prey systems, in order to assess the impact of prey dormancy on the competition…
This paper explores a novel connection between a thermodynamic and a dynamical systems perspective on emergent dynamical order. We provide evidence for a conjecture that Hamiltonian systems with mixed chaos spontaneously find regular…
The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order…
We introduce the $\alpha$-Gauss-Logistic map, a new nonlinear dynamics constructed by composing the logistic and $\alpha$-Gauss maps. Explicitly, our model is given by $x_{t+1} = f_L(x_t)x_t^{-\alpha} - \lfloor f_L(x_t)x_t^{-\alpha} \rfloor…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…