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We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…
Behavioural differences may arise in the absence of genetic or environmental variation. Chaotic dynamics may influence behavioural development, and so this among-individual variation. We discuss methods and experimental designs to test this…
We study the effect of extrinsic noise in metabolic networks. We introduce external random fluctuations at the kinetic level, and show how these lead to a stochastic generalization of standard Metabolic Control Analysis. While Summation and…
We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…
In this chapter the complex systems are discussed in the context of economic and business policy and decision making. It will be showed and motivated that social systems are typically chaotic, non-linear and/or non-equilibrium and therefore…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
We consider long-time behavior of dynamical systems perturbed by a small noise. Under certain conditions, a slow component of such a motion, which is most important for long- time evolution, can be described as a motion on the cone of…
Chaos is a fundamental phenomenon in nonlinear dynamics, manifesting as irregular and unpredictable behavior across various physical systems. Among the diverse routes to chaos, intermittent chaos is a distinct transition pathway,…
Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…
Causal states are minimal sufficient statistics of prediction of a stochastic process, their coding cost is called statistical complexity, and the implied causal structure yields a sense of the process' "intrinsic computation". We discuss…
Understanding under which conditions the increase of systems complexity is evolutionary advantageous, and how this trend is related to the modulation of the intrinsic noise, are fascinating issues of utmost importance for synthetic and…
Our topic is performance differences between using random and chaos for particle swarm optimization (PSO). We take random sequences with different probability distributions and compare them to chaotic sequences with different but also with…