A hunter-gatherer-farmer population model: new conditional symmetries and exact solutions with biological interpretation. (English) Zbl 1504.35021
Summary: New \(Q\)-conditional (nonclassical) symmetries and exact solutions of the hunter-gatherer-farmer population model proposed by K. Aoki et al. [Theor. Popul. Biol. 50, No. 1, 1–17 (1996; Zbl 0856.92026)] are constructed. The main method used for the aforementioned purposes is an extension of the nonclassical method for system of partial differential equations. An analysis of properties of the exact solutions obtained and their biological interpretation are carried out. New results are compared with those derived in recent studies devoted to the same model.
MSC:
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35C05 | Solutions to PDEs in closed form |
| 35K40 | Second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
reaction-diffusion system; population dynamics; exact solution; conditional symmetry; nonclassical symmetryCitations:
Zbl 0856.92026Software:
ReLieReferences:
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