# Oscillations And Traveling Waves In Chemical Systems Pdf

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- Computational simulation of Belousov–Zhabotinskii oscillating chemical reaction
- Emergence of traveling waves in linear arrays of electromechanical oscillators
- Mathematical modeling of a self-oscillating chemical reaction catalyzed by ferroin

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.

## Computational simulation of Belousov–Zhabotinskii oscillating chemical reaction

Victoria E. Deneke, Stefano Di Talia; Chemical waves in cell and developmental biology. J Cell Biol 2 April ; 4 : — Many biological events, such as the propagation of nerve impulses, the synchronized cell cycles of early embryogenesis, and collective cell migration, must be coordinated with remarkable speed across very large distances. Such rapid coordination cannot be achieved by simple diffusion of molecules alone and requires specialized mechanisms.

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. Sergei Trofimchuk, Vitaly Volpert.

## Emergence of traveling waves in linear arrays of electromechanical oscillators

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.

## Mathematical modeling of a self-oscillating chemical reaction catalyzed by ferroin

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.

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.

*Traveling wave solutions of a chemotaxis model with a reaction term are studied.*

#### Acknowledgments

В комнате творилось нечто невообразимое. Техники обнимали друг друга, подбрасывая вверх длинные полосы распечаток. Бринкерхофф обнимал Мидж. Соши заливалась слезами. - Джабба, - спросил Фонтейн, - много они похитили.

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Request PDF | Oscillations and traveling waves | A very important class of shell [5] It is now readily accepted that some nonlinear chemical, important for all catalytic processes whether in living or non-living systems.

Catalyst, Co-ion and the media effect on the oscillatory behavior of resorcinol in the BZ reaction.

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