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Chaotic systems, presenting complex and non-reproducible dynamics, may be found in nature from the interaction between planets to the evolution of the weather, but can also be tailored using current technologies for advanced signal…
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in…
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
We use physical principles to derive a water wheel model under the assumption of an asymmetric water wheel for which the water inflow rate is in general unsteady (modeled by an arbitrary function of time). Our model allows one to recover…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
In the chaotic Lorenz system, Chen system and R\"ossler system, their equilibria are unstable and the number of the equilibria are no more than three. This paper shows how to construct some simple chaotic systems that can have any…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
This paper presents a novel study on gas-like models for economic systems. The interacting agents and the amount of exchanged money at each trade are selected with different levels of randomness, from a purely random way to a more chaotic…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach…
The process of technological change can be regarded as a non-deterministic system governed by factors of a cumulative nature that generate cyclical phenomena. In this context, the process of growth and decline of technology can be…
Order can spontaneously emerge from seemingly noisy interactions between biological agents, like a flock of birds changing their direction of flight in unison, without a leader or an external cue. We are interested in the generic conditions…
In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved…
We investigate the emergence of synchronization in a network of coupled chaotic macroeconomic systems. Each node represents an economy characterized by three key variables savings, gross domestic product (GDP), and foreign capital inflows.…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…
Atmospheric weather systems are coherent structures consisting of discrete cloud cells forming patterns of rows/streets, mesoscale clusters and spiral bands which maintain their identity for the duration of their appreciable life times in…