Parametric portraits of travelling waves of population models with polynomial growth and auto-taxis rates

Nonlinear Analysis: Real World Applications

Volumn 1, Issue 1, 2000, Pages 123-136

  Berezovskaya, F ^a   Karev, G ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

Auto model system; Bifurcations; Chemotaxis; Growth taxis diffusion equation; Population; Travelling wave

Indexed keywords

EID: 0034147307     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00396-X     Document Type: Article

References (18)

1. W.C. Allee, Animal Aggregation: A Study in General Sociology, Chicago Press, Chicago, 1931.
2. V.I. Arnold, Geometrical Methods of Ordinary Differential Equations, Springer, New York, 1983.
3. G.I. Barenblatt, Ya.B. Zeldovich, Intermediate asymptotics in mathematical physics, Uspekhi Matematicheskikh Nauk 26 (2) (1971) 115.
4. F.S. Berezovskaya, Parameter analysis of "travelling waves" in polynomial equations "reaction-diffusion-convection", Proceedings of the Fifth International Conference Mathematics, Computer, Education, Vol. 2, Moscow State University, 1998, p. 22.
5. F.S. Berezovskaya, G.P. Karev, Travelling waves in polynomial population models, Dokl. Mathematica 60 (2) (1999) 295.
6. F.S. Berezovskaya, A.S. Isaev, G.P. Karev, R.G. Khlebopros, Role of taxis in forest insect dynamics, Dokl. Biological Sci. 365 (1999) 148.
7. R.I. Bogdanov, Versal deformations of a singular point on the plane in the case of zero eigenvalues, Funct. Anal. Appl. 9 (1975) 144.
8. F. Dumortier, R. Rossarie, J. Sotomayor, Generic 3-parameters families of planar vector fields, unfoldings of saddle, focus and elliptic singularities with nilpotent linear parts, Lecture Notes in Mathematics, Vol. 1480, Springer, Berlin, 1991.
9. R.A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics 7 (1937) 355.
10. A.N. Kolmogorov, I.G. Petrovsky, N.S. Piskunov, Investigation of equation of diffusion joint with increase of an amount of substance, and it application to one biological problem, Bull. MSU 1 (6) (1937) 1.
11. Yu.A. Kuznetsov, Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, Vol. 112, Springer, New York, 1998.
12. Y.A. Kuznetsov, V.N. Biktashev, E.A. Aponina, M.Ya. Antonovsky, Cross-diffusion model of the forest boundary dynamics, Problems of Ecological Monitoring and Modeling of Ecosystems, Vol. XVI, Gidrometeoizdat, S.-Petersburg, 1996, p. 213.
13. A. Monk, H.G. Othmer, Cyclic AMP oscillations in suspensions of Dictyostelium discoideum, Philos. Trans. Roy. Soc. London 323 (1989) 185.
14. J.D. Murray, Mathematical Biology, Springer, Berlin, 1993.
15. A. Okubo, Diffusion and Ecological Problems: Mathematical Models, Springer, New York, 1980.
16. H.G. Othmer, A. Stevens, Aggregation, blow-up and collapse: The abcs of taxis in reinforced random walks, SIAM J. Appl. Math. 57 (4) (1997) 1044.
17. A.A. Samarsky, A.P. Mikhailov, Mathematical Modeling, Nauka, Moscow, 1997.
18. Wei-Ming Ni, Diffusion, cross-diffusion and their spike-layer steady states, Notices 45 (9) 1998.