Related papers: Beyond Chaos
In [Adv. Math., 267(2014), 277-306], Cheskidov and Lu develop a new framework of the evolutionary system that deals directly with the notion of a uniform global attractor due to Haraux, and by which a trajectory attractor is able to be…
The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption of gravitational radiation is investigated. This work extends our previous results on transient chaos in the planar case to the three…
Discrete-time replicator map is a prototype of evolutionary selection game dynamical models that have been very successful across disciplines in rendering insights into the attainment of the equilibrium outcomes, like the Nash equilibrium…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
Predator-prey coevolution is commonly thought to result in reciprocal arms races that produce increasingly extreme and complex traits. However, such directional change is not inevitable. Here, we provide evidence for a previously…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
Recent work has shown that pairwise interactions may not be sufficient to fully model ecological dynamics in the wild. In this letter, we consider a replicator dynamic that takes both pairwise and triadic interactions into consideration…
Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…
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…
The interaction of an open system $\s$ with a pre- and post-selected environment is studied. In general, under such circumstances $\s$ can not be described in terms of a density matrix, {\it even when $\s$ in not post-selected}. However, a…
The concept of hierarchy in complex systems is tightly linked to co-evolutionary processes. We propose here to explore it in the case of the co-evolution between transportation networks and territories. More precisely, we extend a…
Prior work on generating explanations in a planning and decision-making context has focused on providing the rationale behind an AI agent's decision making. While these methods provide the right explanations from the explainer's…
The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how,…
Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are…
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…
Consider a finite number of balls initially placed in $L$ bins. At each time step a ball is taken from each non-empty bin. Then all the balls are uniformly reassigned into bins. This finite Markov chain is called Repeated Balls-into-Bins…
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…