Miki U. Kobayashi

Scytale decodes chaos: A method for estimating unstable symmetric solutions

A method for estimating a period of unstable periodic solutions is suggested in continuous dissipative chaotic dynamical systems. The measurement of a minimum distance between a reference state and an image of transformation of it exhibits a characteristic structure of the system, and the local minima of the structure give candidates of period and state of corresponding symmetric solutions. Appropriate periods and initial states for the Newton method are chosen efficiently by setting a threshold to the range of the minimum distance and the period.

Determination of chaotic dynamical correlations in terms of unstable periodic orbits

For low-dimensional chaotic systems, we find that time correlation functions can be accurately approximated by a single unstable periodic orbit. The method of this determination consists of the following two steps. First, the time correlation functions are expanded in terms of static correlation functions by making use of the expansion method recently proposed by one of the authors [H. Fujisaka, Prog. Theor. Phys. 114 (2005), 1]. Second, the static quantities are approximated in terms of an unstable periodic orbit embedded in the strange attractor. Thus the dynamical correlation functions in chaotic systems can be determined in terms of an unstable periodic orbit. Furthermore, applying this method to low-dimensional chaotic models, we prove the usefulness of the present approach.

Time-delayed feedback control of diffusion in random walkers

Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic process, i.e., a random walk and observe its diffusion phenomenon with time delayed feedback. Surprisingly, the diffusion coefficient decreases with increasing the delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying the time-delay feedback to a molecular dynamics model.

Time Correlation Calculation Method Based on Delayed Coordinates

An approximate calculation method of time correlations by use of delayed coordinate is proposed. For a solvable piecewise linear hyperbolic chaotic map, this approximation is compared with the exact calculation, and an exponential convergence for the maximum time delay M is found. By use of this exponential convergence, the exact result for M →∞ is extrapolated from this approximation for the first few values of M . This extrapolation is shown to be much better than direct numerical simulations based on the definition of the time correlation function. As an application, the irregular dependence of diffusion coefficients similar to Takagi or Weierstrass functions is obtained from this approximation, which is indistinguishable from the exact result only at M = 2. The method is also applied to the

Zinc deficiency causes delayed ATP clearance and adenosine generation in rats and cell culture models

Zinc deficiency causes myriad pathophysiological symptoms, but why distinct phenotypes are generated by zinc deficiency remains unclear. Considering that several ectoenzymes involved in purinergic signaling through extracellular adenine-nucleotide hydrolysis possess zinc ions in their active sites, and disorders in purinergic signaling result in diverse diseases that are frequently similar to those caused by zinc deficiency, herein we examine whether zinc deficiency affects extracellular adenine-nucleotide metabolism. Zinc deficiency severely impairs the activities of major ectoenzymes (ENPP1, ENPP3, NT5E/CD73, and TNAP), and also strongly suppresses adenine-nucleotide hydrolysis in cell-membrane preparations or rat plasma, thereby increasing ATP and ADP levels and decreasing adenosine levels. Thus, zinc deficiency delays both extracellular ATP clearance and adenosine generation, and zinc modulates extracellular adenine-nucleotide metabolism. Since the finely tuned balance between extracellular adenine nucleotides and adenosine is critical for purinergic signaling, these findings provide a novel insight into why zinc deficiency results in diverse symptoms.Taka-aki Takeda et al. find that zinc deficiency impairs adenine nucleotide metabolism in both cell and rat models leading to delays in extracellular ATP clearance and adenosine generation. The results show that zinc deficiency affects purinergic signaling and may explain why zinc deficiency in humans results in diverse symptoms.

Chaotic interfaces in a parametrically forced system

The structure and motion of a single interface exhibiting chaotic behavior are investigated in one-dimensional parametrically forced complex Ginzburg-Landau equation. Several kinds of interfaces are classified by their dynamical behavior connected with the symmetries.