In this paper I consider the concept of time in a general way as daily human and then within physics with relation to mathematics. arrow focus attention on quantum mechanics, its particular peculiarities, examining important concepts like temporal asymmetry, complexity, decoherence, irreversibility, information theory, chaos theory. conclusion notion connected new theory progress, called “Primo...

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

s (Listed in alphabetically order of author’s surname) Kazuyuki Aihara Institute of Industrial Science, University of Tokyo CHAOS AND BIFURCATIONS IN THE HODGKIN-HUXLEY EQUATIONS AND SQUID GIANT AXONS Chaos, or deterministic chaos, is ubiquitous in nonlinear dynamical systems of the real world, including biological systems. Nerve membranes have their own nonlinear dynamics which generate and pr...

In the present paper we show that inhomogeneity of a continuous self-sustained oscillating medium can be a reason for the onset of chaotic behavior. It has been established that temporal chaotic dynamics typically arises in the medium with a linear mismatch of the natural frequency along a spatial coordinate, whereas a chaotic regime is not characteristic for the medium with randomly distribute...

A sensitivity and correlation analysis of EEG sensors influenced by uncertain conductivity is conducted. We assume a three layer spherical head model with different and random layer conductivities. This randomness is modeled by Polynomial Chaos (PC). On average, we observe the least influenced electrodes along the great longitudinal fissure. Also, sensors located closer to a dipole source, are ...

In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are innnite-dimensional analogues of Axiom A systems. Our main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. In the rst paper we develop a stable manifold theory for such systems ...

In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are innnite-dimensional analogues of Axiom A systems. Our main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. In this paper we develop a stable manifold theory for such systems as ...

Based on the Melnikov method, we investigate chaotic behaviors in extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations. Our results show that perturbation coming from thermal quench of spinodal region diagram may cause chaos only when amplitude is above critical value, which involves angular momentum . Under perturbation, however,...

We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Nav...

Temporal seizures due to hippocampal origins are very common among epileptic patients. Presented is a novel seizure prediction approach employing correlation and chaos theories. The early identification of seizure signature allows for various preventive measures to be undertaken. Electro-encephalography signals are spectrally broken down into the following sub-bands: delta; theta; alpha; beta; ...