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1. (1) are referred to as the reaction-diffusion equations.
2. The reaction-diffusion equations form the basis for the interpretation of the experiments reviewed above.
3. This places reaction-diffusion systems in the forefront for understanding the origin of endogenous rhythmic and patterning phenomena observed in nature and in technological applications.
4. All elements at our disposal indicate that there exists no exhaustive list and universal classification of the full set of solutions of reaction-diffusion equations.
5. We first study the effect of the original state and main parameters D, K and time t on the dynamic concentration pattern of the reaction-diffusion system.
6. When the K/D ratio increases, the reaction becomes dominant in the reaction-diffusion system and the time needed to reach steady state drops quickly.
7. To compare the computation time, we run the FEM simulation and CNN prediction to solve the reaction-diffusion equation with the same input configurations for 1,000 time steps.
8. Reaction–diffusion systems are naturally applied in chemistry.
9. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential equations.
10. In addition to the reaction-diffusion equation parameters, you can also adjust the uniform scale, rotation, and X/Y offset of the image for different effects.
11. Well,if you feel that way, you will become a big fan of the reaction-diffusion systems we discussed in Section 13.6.
12. This shortcut in linear stability analysis is made possible thanks to the clear separation of reaction and diffusion terms in reaction-diffusion systems.
13. Firstly, we 'vectorize' this analysis to be applicable for a class of reaction–diffusion equations, characterized by certain conditions.
14. A reaction-diffusion model motivated by Proteus mirabilis swarm colony development is presented and analyzed in this work.
15. The theoretical results and the linear stability of these spot equilibria are confirmed by solving the nonlinear evolution of the Brusselator reaction-diffusion model by numerical means.
16. The approach adopted is extended to solve a class of non-linear reaction-diffusion equations in two-space dimensions known as the "Brusselator" system.
17. We review a series of key travelling front problems in reaction–diffusion systems with a time-delayed feedback, appearing in ecology, nonlinear optics and neurobiology.
18. In this work, we limit our review to scalar reaction–diffusion equations and concentrate on monostable and bistable front solutions.
19. Mathematical reaction–diffusion models are proposed to describe or predict the fate of some particular invasions.
20. Based on these common properties, we developed conceptual models of a mass conserved reaction–diffusion system with diffusion–driven instability.
21. Figure 2 shows one such set of patterns, obtained from a random initial distribution in a system that evolves according to a system of reaction-diffusion equations called the Gray-Scott model.
22. This suggests the intriguing possibility of organizing amorphous computing systems by starting with the particles in a random state and solving a discrete analog of a reaction-diffusion system.
23. They have been encountered in a number of physical systems and model equations but have only rarely been found in reaction-diffusion systems to date.
24. We present here examples of several types of localized patterns found in reaction-diffusion systems.

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• ID : Q901210

Spacy 패턴 목록

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