Dynamics of a reaction-diffusion equation with nonlocal inhibition

Physica D: Nonlinear Phenomena

Volumn 134, Issue 1, 1999, Pages 94-110

  Raquepas, J B ^a   Dockery, J D ^b  

^a UNIVERSITY OF UTAH   (United States)

^b MONTANA STATE UNIVERSITY   (United States)

Author keywords

Bifurcation theory; Center manifolds; Reaction diffusion equations

Indexed keywords

EID: 0006029578     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00064-0     Document Type: Article

References (16)

1. R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
2. J. Carr, Applications of Center Manifold Theory, Springer, New York, 1980.
3. S. Chow, J. Hale, Methods of Bifurcation Theory, Springer, New York, 1982.
4. Fiedler B., Polacik P. Complicated dynamics of a scalar reaction diffusion equation with a nonlocal term. Proceedings of the Royal Society of Edinburgh. 115:1990;167-192.
5. Frietas P. Bifurcation and stability of stationary solutions of a nonlocal scalar reaction-diffusion equation. Journal of Dynamics and Differential Equations. 6:1994;613-629.
6. Frietas P. A nonlocal Sturm-Liouville eigenvalue problem. Proceedings of the Royal Society of Edinburgh. 124:1994;169-188.
7. Fuji H., Mimura M., Nishiura Y. A picture of the global bifurcation diagram in ecological interacting and diffusing systems. Physica. 5:1982;1-42.
8. M. Golubitsky, D. Schaeffer, Singularities and Groups in Bifurcation Theory, Springer, New York, 1984.
9. J. Hale, Asymptotic behavior of dissipative systems: AMS Mathematical surveys and monographs, No. 25, American Mathematical Society, Providence, RI, 1988.
10. D. Henry, Geometric Theory of Semilinear Parabolic Equations: Lecture Notes in Mathematics, vol. 840, Springer, Berlin, 1981.
11. Keener J.P. Secondary bifurcations in nonlinear diffusion reaction equations. Studies in Applied Mathematics. 55:1976;187-211.
12. Keener J.P. Secondary bifurcations and multiple eigenvalues. SIAM Journal of Applied Mathematics. 37:1979;330-349.
13. J. Murray, Mathematical Biology, Springer, Berlin, 1986.
14. Nishiura Y. Global structure of bifurcating solutions of some reaction-diffusion systems. SIAM Journal of Mathematical Analysis. 4:1982;555-593.
15. A. Pazzy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.
16. E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. I: Fixed Point Theorems, Springer, New York, 1986.