Order in time and space with the Brusselator system

Example 13.4 Order in time and space with the Brusselator system The Brusselator model with unequal diffusion may produce order in time and space. When the concentrations of. 1 and B are controlled, the one-dimensional approach to complex reaction-diffusion systems with the spatial coordinate r under isothermal conditions yields the kinetic equations forXand Y (Eqs. (12.98) and (12.99)) 

For a specified value for. 4 and some variation of B if one of the eigenvalues becomes positive, then Det 0, and the system becomes unstable, and the propagating wave or the Turing structure occur 

At the start, the cycle begins with a certain amount of Ce+4 ions. The second reaction provides Br- ions, which inhibit the first reaction. This leads to an increase in concentration of Ce+3. After reaching a certain amount of Ce+3, the oxidation reaction starts, since little Ce+4 remains. The system can no longer produce sufficient Br to inhibit the reaction, and Ce+3 decreases rapidly, producing Ce+4 until the cycle is completed. It is possible to maintain indefinite oscillations with constant frequency in a continuous flow stirred reactor into which bromate, malonic acid, and cerium catalyst are being supplied at a uniform rate. 

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Example 13.4 Order in time and space with the Brusselator system... 

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