Related papers: Beyond Chaos
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…
Population dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here, we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…
Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We…
A one-parameter family of time-reversible systems on $\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the…
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…
This letter seeks to illuminate the profound connection between complexity, self-organization, emergent behaviour, pattern formation, and entropy concepts that are foundational to understanding our universe. By examining these ideas through…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
Understanding how cooperative behaviours can emerge from competitive interactions is an open problem in biology and social sciences. While interactions are usually modelled as pairwise networks, the units of many real-world systems can also…
The present paper presents a new general conception of interaction between physical systems, differing significantly from that of both classical physics and quantum physics as generally understood. We believe this conception could provide…
New features related to collective properties generated in the systems driven by random dynamics are observed and their implications for further understanding of interplay between coherence and chaos are discussed.
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…
We examine the effects of symmetry--preserving and breaking interactions in a drive--response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find…
While modern physics and biology satisfactorily explain the passage from the Big Bang to the formation of Earth and the first cells to present-day life, respectively, the origins of biochemical life still remain an open question. Since…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded…
We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, this family exhibits suspended horseshoes and persistent strange attractors.…
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation may split into an initial exponential decrease, characterized by the maximal Lyapunov…