We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies of these states. We find that this model exhibits strong, weak or no temperature chaos depending on the value of an exponent. This allows us to write a genera...

The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent (exponential dynamical instability) is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov exponent, as a unified characterization of nonexponential and exponential dynamical instabilities in one-dimensional maps. Ch...

Transient chaos is a common phenomenon in nonlinear dynamics of many physical, biological, and engineering systems. In applications it is often desirable to maintain sustained chaos even in parameter regimes of transient chaos. We address how to sustain transient chaos in deterministic flows. We utilize a simple and practical method, based on extracting the fundamental dynamics from time series...

Chaos theory and models related to non-linear dynamic systems has increased in importance in recent decades. In fact, chaos is one of the concepts that has most rapidly expanded in research topics. Chaos is ordinarily disorder or confusion; scientifically, it represents a disarray connection, but basically, it involves much more than that. Change and time are closely linked, and they are essent...

chaotic circuits coupled by one resistor. By carrying out that our very simple coupled circuit can exhibit spatiotemporal chaos as well as quasi-synchronizations of chaos in spite of tha t the number of chaotic subcircuit.s is only four. We consider that our model would be good model to clarify mechanism and characteristics of spatiotemporal chaos because it is the simplest real physical system...

We consider the effects of parametric perturbation on the onset of chaos in different dynamical systems. Favoring or suppression of chaos was observed depending on the phase or the frequency of the periodic perturbation. A lowering of the threshold of chaos was observed in an electronic device simulating a Josephson-Junction model and the suppression of chaos was obtained in a bistable mechanic...

Many systems in nature are governed by a large number of agents that interact nonlinearly through complex feedback loops. When the networks are sufficiently large and interconnected, they typically exhibit self-organization and chaos. This paper examines the prevalence and degree of chaos on large unweighted recurrent networks of ordinary differential equations with sigmoidal nonlinearities and...