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.

Project Earth Conservation

Project Earth Conservation

Get All The Support And Guidance You Need To Be A Success At Helping Save The Earth. This Book Is One Of The Most Valuable Resources In The World When It Comes To How To Recycle to Create a Better Future for Our Children.

Get My Free Ebook


Post a comment