Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model

Abstract

Q-conditional (nonclassical) symmetries of the known three-component reaction-diffusion system [K. Aoki et al Theor. Pop. Biol. 50(1) (1996)] modeling interaction between farmers and hunter-gatherers are constructed for the first time. A wide variety of Q-conditional symmetries are found in an explicit form and it is shown that these symmetries are not equivalent to the Lie symmetries. Some operators of Q-conditional (nonclassical) symmetry are applied for finding exact solutions of the reaction-diffusion system in question. Properties of the exact solutions (in particular, their asymptotic behaviour) are identified and possible biological interpretation is discussed.

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Cited by in corpus (3)

• Construction and application of exact solutions of the diffusive Lotka-Volterra system: a review and new results
• Exact Nonclassical Symmetry Solutions of Lotka-Volterra Type Population Systems
• A hunter-gatherer-farmer population model: new conditional symmetries and exact solutions with biological interpretation