Stochastic process of pragmatic information for 2D spiral wave turbulence in globally and locally coupled Alief-Panfilov oscillators

Abstract

Abstract. Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.

Taking drift-diffusion analysis from the study of turbulent flows to the study of particulate matter smog and air pollutants dynamics

“…From the trajectories Y n , scatter plots for each month m showing Y n (τ + 1) versus Y n (τ) were obtained. From the scatter plots, the drift functions f were determined by means of the 3 different approximations defined by equations (4), (5) and (6). Figure 2 shows the drift functions f (Y, m) thus obtained for PM 10 for the first four months of the year, January to April.…”

“…In order to validate the model, we tested the residuals occurring in equation (6). We determined the first ten lag-s autocorrelation coefficients of the residuals for each trajectory Y n (τ).…”

“…The method was in part motivated by the self-similarity hypothesis of turbulent flows that in its own merit has been investigated in various systems (see e.g., [2]). In recent years, various studies have examined turbulence using the drift-diffusion analysis approach [3][4][5][6], see also [7]. However, the method turned out to have a broad spectrum of applications (for a review see [7]).…”