Abstract
Hyperbolic reaction-diffusion equations are discussed with the example of the Brusselator in this paper. Their behavior is compared with that of the parabolic reaction-diffusion equations conventionally used in connection with oscillating chemical reactions and chemical waves. It is shown by using the example of the Brusselator that an approximate dispersion relation computed from the hyperbolic reaction-diffusion equations has a qualitatively correct wave number dependence whereas the parabolic equations do not yield a dispersion relation when a similar method is used. It is also shown that chaotic solutions can arise in the case of hyperbolic reaction-diffusion equations. Linear stability characteristics can be quite different in the two cases of evolution equations.
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