We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential can lead to modifications in semiclassical approximations for spectral statistics that persist in the semiclassical limit ~ → 0. This result is obtained by de...

We revive the long standing Boltzmann-Loschmidt polemic which confronts irreversible Thermodynamics with reversible Mechanics. While this is solved within classical physics by the theory of Chaos, until now, there is no quantum de ̄nition of dynamical chaos. A nice possibility o®ered by NMR is to invert the direction of time (quantum Loschmidt daemon) in a many-body spin system. The e±ciency of ...

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It is demonstr ated th at the chaotic properties of neural networks (in this case networks defined by the generalized delta procedur e) can be used to improve th eir learning performance. By adapt ively varying the learning-rate parameter an annealing mechanism can be introduced that is founded in chaos. T he prop osed mechanism, chaos-based learning, provides faster convergence than standard b...

A mathematically simple example of a high-dimensional (many-species) Lotka-Volterra model that exhibits spatiotemporal chaos in one spatial dimension is described. The model consists of a closed ring of identical agents, each competing for fixed finite resources with two of its four nearest neighbors. The model is prototypical of more complicated models in its quasiperiodic route to chaos (incl...

We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and vice versa. We further constructed an improved mass-sprig model for the same system on the basis of data obtained from the fluid dynamical computations. A det...

We extend a previous Gause-type predator–prey model to include a general monotonic and bounded seasonally varying functional response. The model exhibits rich dynamical behaviour not encountered when the functional response is not seasonally forced. A theoretical analysis is performed on the model to investigate the global stability of the boundary equilibria and the existence of periodic solut...

today we are facing with a turbulent world full of complexity and change. contemporary problems are too complicated for rational, logical solutions. they admit insights, not answers. chaos theory is a solution to reveal insights into the structure and the dynamics of complex systems. chaos theory is in formative stage, but we can use it in management practices. this article is about application...

analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. this paper compares the performance of chaos theory with anfis model and discusses ...

chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...