Further Reading

Afraimovich V and Hsu S (2003) Lectures on Chaotic Dynamical Systems. Providence: American Mathematical Society and International Press.

Baurmann M, Gross T, and Feudel U (2006) Instabilities in spatially extended predator-prey systems: Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. Journal of Theoretical Biology 245, doi: 10.1016/j.jtbi.2006.09.036.

Berryman A (1992) The origins and evolution of predator-prey theory. Ecology 73: 1530-1535.

Cushing JM, Costantino RF, Dennis B, etal. (1998) Nonlinear population dynamics: Model, experiment and data. Journal of Theoretical Biology 194: 1-9.

Doebeli M (1994) Intermittent chaos in population dynamics. Journal of Biological Systems 166: 325-330.

Gross T (2004) Population Dynamics: General Results from Local Analysis. PhD Thesis, Tonning: Der Andere Verlag, Germany.

Hardenberg J, Meron E, Shachak M, and Zarmi Y (2001) Diversity of vegetation patterns and desertification. Physical Review Letters 87: 198101.

Hirsch MW, Smale S, and Devaney RL (2004) Differential Equations, Dynamical Systems, and an Introduction to Chaos. San Diego: Elsevier.

Kendall BE (2001) Nonlinear dynamics and chaos. In: Anne O'Daly (ed.) Encyclopedia of Life Sciences Vol. 13: pp. 255-262. London: Nature Publishing Group.

King AA and Schaffer WM (2001) The geometry of a population cycle: A mechanistic model of snowshoe hare demography. Ecology 82: 814-830.

Klausmeier CA (1999) Regular and irregular patterns in semi-arid vegetation. Science 284: 1826-1828.

Leppanen T (2004) Computational Studies of Pattern Formation in Turing systems. PhD Thesis. Espoo: Helsinki University of Technology, Finland.

Li Z, Wang W, and Wang H (2006) The dynamics of a Beddington-type system with impulsive control strategy. Chaos, Solitons and Fractals 29: 1229-1239.

Lu Q (1995) Bifurcation and Singularity (in Chinese). Shanghai: Shanghai Scientific and Technological Education Publishing House.

May RM (1974) Biological populations with non-overlapping generations: Stable points, stable cycles, and chaos. Science 186: 645-647.

May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261: 459-467.

May RM and Oster GF (1976) Bifurcations and dynamic complexity in simple ecological models. American Naturalist 110: 573-599.

Medvinsky AB, Petrovskii SV, Tikhonova IA, Malchow H, and Li B (2004) Spatiotemporal complexity of plankton and fish dynamics. SIAM Review 44: 311C370.

Milton JG, Longtin A, Beuter A, et al. (1989) Complex dynamics and bifurcation in neurology. Journal of Biological Systems 138: 129-147.

Murray JD (2003) Mathematical Biology, 3rd edn. Berlin: Springer.

Schuster S and Marhl M (2001) Bifurcation analysis of calcium oscillations: Time-scale separation, canards and frequency lowering. Journal of Biological Systems 9: 291-314.

Segel L and Jackson J (1972) Dissipative structure: An explanation and an ecological example. Journal of Theoretical Biology 37: 545-559.

Seydel R (1994) Practical Bifurcation and Stability Analysis. New York: Springer.

Turing A (1952) The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London-B 237(B641): 37-72.

Wang H, Li Z, and Wang W (2006) Dynamic complexity of a

Beddington-type system with impulsive perturbations. Differential Equations and Dynamical Systems 14: 57-79.

Wang W, Liu Q, and Jin Z (2007) Spatiotemporal complexity of a ratio-dependent predator-prey system. Physical Review E 75: 051913.

Wang W, Wang H, and Li Z (2006) Chaotic behavior of a three-species Beddington-type system with impulsive perturbations. Chaos, Solitons and Fractals doi:10.1016/j.chaos.2006.09.013.

Wang W, Wang H, and Li Z (2007) The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy. Chaos, Solitons and Fractals 32(5): 1772-1782.

Wang X, Wang W, and Lin X (2006) Chaotic behavior of a Watt-type predator-prey system with impulsive control strategy. Chaos, Solitons and Fractals doi:10.1016/j.chaos.2006.09.050.

Wang W, Wang X, and Lin Y (2006) Complicated dynamics of a predator-prey system with Watt-type functional response and impulsive control strategy. Chaos, Solitons and Fractals doi: 10.1016/j.chaos.2006.10.032.

Xiao D and Zhu H (2006) Multiple focus and Hopf bifurcations in a predator-prey system with nonmonotic functional response. SIAM Journal of Applied Mathematics 66: 802-819.

Yang L, Anatol MZ, and Epstein IR (2004) Stable squares and other oscillatory Turing patterns in a reaction-diffusion model. Physical Review Letters 92: 198303.

Was this article helpful?

0 0
Worm Farming

Worm Farming

Do You Want To Learn More About Green Living That Can Save You Money? Discover How To Create A Worm Farm From Scratch! Recycling has caught on with a more people as the years go by. Well, now theres another way to recycle that may seem unconventional at first, but it can save you money down the road.

Get My Free Ebook

Post a comment