Related papers: Topological characterisation of a chaotic attracto…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
The chaotic properties of Newton-Leipnik system are discussed from the view point of strange attractors. Previously, two strange attractors of this system were illustrated which occured from two different initial conditions under the same…
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…
For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities…
We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic nonalgebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we…
This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
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…
The R\"ossler system is one of the best known chaotic dynamical systems, generating a chaotic attractor which, by the numerical evidence, arises by a period-doubling route to chaos. In this paper we state and prove a topological criterion…
When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: parity, global…
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…
Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
We study numerically chaotic behavior associated with a hyperbolic strange attractor of Plykin type in the model of Hunt, an artificially constructed dynamical system with continuous time. There are presented portraits of the attractor,…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
We consider piecewise linear discrete time macroeconomic models, which possess a continuum of equilibrium states. These systems are obtained by replacing rational inflation expectations with a boundedly rational, and genuinely sticky,…