File Name: oscillations and traveling waves in chemical systems .zip
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Catalyst, Co-ion and the media effect on the oscillatory behavior of resorcinol in the BZ reaction.
Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. Traveling waves of mechanical actuation provide a versatile strategy for locomotion and transport in both natural and engineered systems across many scales.
Citation: Sergei Trofimchuk, Vitaly Volpert. Traveling waves in delayed reaction-diffusion equations in biology[J]. Mathematical Biosciences and Engineering, , 17 6 : Article views PDF downloads 38 Cited by 0. Figures 4.
The suitability of computational simulation of the Belousov—Zhabotinskii oscillating chemical reaction by differential kinetic methodology for resolving nonlinear multi-component system is demonstrated in this work. The results of computational simulation are consistent with experimental results very well. At the same time, the effect of variables and parameters, especially the rate constant on the oscillation curve, are investigated deeply. A simple method of estimating rate constants is obtained through simulation the concentrations of key components of the system, and then comparison the simulation results with the experimental ones. The reasonable rate constant is also proposed. This is a preview of subscription content, access via your institution. Field, R.
The Bray-Liebhafsky reaction exhibits different nonlinear behaviors during the iodate catalyzed decomposition of acidic hydrogen peroxide in the different conditions. Both the chaotic and regular oscillations were observed. The effect of initial concentration of reactants on the types of oscillations and the initial potential E o were discussed in detail. The possible mechanism of the Bray-Liebhafsky reaction was also approached in this work. Keywords : Bray-Liebhafsky reaction; largest Lyapunov exponent; power spectram; mechanism. The nonlinear chemical phenomena known as "oscillating chemical reaction" are complex dynamic systems that have so farbeen examined mainly in physico-chemical terms in order to elucidate the complex mechanism. Thus, various dynamics regimes including regular oscillations, periodic doubling, quasi-periodicity and deterministic chaos have been explored with a view to their characterization in recent years
Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient — even in the absence of inter-filament hydrodynamic interactions — to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns.
Traveling wave solutions of a chemotaxis model with a reaction term are studied. We investigate the existence and non-existence of traveling wave solutions in certain ranges of parameters. Particularly for a positive rate of chemical growth, we prove the existence of a heteroclinic orbit by constructing a positively invariant set in the three dimensional space. The monotonicity of traveling waves is also analyzed in terms of chemotaxis, reaction and diffusion parameters. Finally, the traveling wave solutions are shown to be linearly unstable. Adler , Chemotaxis in bacteria, Science , 40 , Google Scholar.
Predictive coding is a key mechanism to understand the computational processes underlying brain functioning: in a hierarchical network, higher levels predict the activity of lower levels, and the unexplained residuals i. Because of its recursive nature, we wondered whether predictive coding could be related to brain oscillatory dynamics. First, we show that a simple 2-level predictive coding model of visual cortex, with physiological communication delays between levels, naturally gives rise to alpha-band rhythms, similar to experimental observations. Then, we demonstrate that a multilevel version of the same model can explain the occurrence of oscillatory traveling waves across levels, both forward during visual stimulation and backward during rest. Remarkably, the predictions of our model are matched by the analysis of 2 independent electroencephalography EEG datasets, in which we observed oscillatory traveling waves in both directions.
In mathematics, a periodic travelling wave or wavetrain is a periodic function of one- dimensional space that moves with constant speed. Consequently, it is a special type of spatiotemporal oscillation that is a periodic function of both space and time. Periodic travelling waves play a fundamental role in many mathematical equations, including self-oscillatory systems , [1] [2] excitable systems [3] and reaction—diffusion—advection systems. The mathematical theory of periodic travelling waves is most fully developed for partial differential equations , but these solutions also occur in a number of other types of mathematical system, including integrodifferential equations, [5] [6] integrodifference equations, [7] coupled map lattices [8] and cellular automata [9] [10]. As well as being important in their own right, periodic travelling waves are significant as the one-dimensional equivalent of spiral waves and target patterns in two-dimensional space, and of scroll waves in three-dimensional space. Periodic travelling waves were first studied in the s.
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Я сделал это ради нас обоих. Мы созданы друг для друга.