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Periodic and traveling wave solutions to Volterra-Lotka equations with diffusion. (English) Zbl 0345.92007


MSC:

92D25 Population dynamics (general)
35K55 Nonlinear parabolic equations
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[1] Hadeler, K. P., U. an der Heiden and F. Rothe. 1974. ”Nonhomogeneous Spatial Distribution of Populations.”J. Math. Biol.,1, 165–176. · Zbl 0315.92012
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[4] Kopell, N. and L. N. Howard. 1973. ”Plane Wave Solutions to Reaction-Diffusion Equations.”Stud. Appl. Math.,52, 291–328. · Zbl 0305.35081
[5] Montroll, E. W. 1968. ”Lectures on Nonlinear Rate Equations, Especially Those with Quadratic Nonlinearities.” In:Lectures in Theoretical Physics, 10A. (Ed. A. Barut and W. Brittin) pp. 531–573. New York: Gordon and Breach.
[6] Rinzel, J. and J. B. Keller, 1973. ”Travelling Wave Solutions of a Nerve Conduction Equation.”Biophys. J.,13, 1313–1337.
[7] Rosen, G. 1975. ”Solutions to Systems of Nonlinear Reaction-Diffusion Equations.”Bull. Math. Biol. 37, 277–289. · Zbl 0314.92002
[8] Stakgold, I., D. D. Joseph and D. H. Sattinger, eds. 1973.Nonlinear Problems in the Physical Sciences and Biology. New York: Springer-Verlag. · Zbl 0254.00025
[9] Williams, S. A. and P. L. Chow. 1976. ”Nonlinear Reaction-Diffusion Equations for Interacting Populations,”J. Math. Analy. Appl, to appear.
[10] Zubov, V. 1964.Methods of A. M. Liapunov and Their Applications. Gronigen: Noordhoff.
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