Related papers: Chaos in Topological Spaces
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In…
The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic…
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…
The decay of the overlap between a wave packet evolved with a Hamiltonian H and the same state evolved with H}+$\Sigma $ serves as a measure of the decoherence time $\tau_{\phi}$. Recent experimental and analytical evidence on classically…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
We describe some highlights in the theory of chaos, that started with Poincare (1899). Generic systems have both ordered and chaotic domains. Chaos appears mainly near un- stable periodic orbits. Large chaotic domains are due to resonance…
This talk summarises what is currently understood about the phenomenon that has come to be known as {\it chaotic mixing}. The first part presents a concise statement as to what chaotic mixing actually is, and then explains why it should be…
We consider Gaussian multiplicative chaos measures defined in a general setting of metric measure spaces. Uniqueness results are obtained, verifying that different sequences of approximating Gaussian fields lead to the same chaos measure.…
The notion of primitive chaos was proposed [J. Phys. Soc. Jpn. {\bf 79}, 15002 (2010)] as a notion closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility.…
There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers (e.g., Popper), it is possible to understand that the two concepts are completely unrelated. In few words we can say…
We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and…
We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…
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,…
We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…
We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete…
According to the standard model of cosmology, the arrangement of matter in the cosmos on scales much larger than galaxies is entirely specified by the initial conditions laid down during inflation. But zooming in by dozens of orders of…
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…
Classical chaos refers to the property of trajectories to diverge exponentially as time tends to infinity. It is characterized by a positive Lyapunov exponent. There are many different descriptions of quantum chaos. The one related to the…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
It is argued that, if a regular Hamiltonian is perturbed by a term that produces chaos, the onset of chaos is shifted towards larger values of the perturbation parameter if the unperturbed spectrum is degenerate and the lifting of the…