TY - GEN AU - Murray, James D. TI - Mathematical biology 1: an introduction SN - 9781475777093 U1 - 570.15118 PY - 2002/// CY - London PB - Springer KW - Biology--Mathematical models KW - Biomathematics KW - Biomedical engineering N1 - Continuous population models for single species -- Discrete population models for a single species -- Continuous models for interacting populations -- Discrete growth models for interacting populations -- Reaction kinetics -- Biological oscillators and switches -- Belousov-Zhabotinskii reaction -- Perturbed and coupled oscillators and black holes -- Reaction diffusion, chemotaxis and non-local mechanisms -- Oscillator generated wave phenomena and central pattern generators -- Biological waves: single species model -- Biological waves: multi-species reaction diffusion models -- Travelling waves in reaction diffusion systems with weak diffusion: analytical techniques and results -- Spatial pattern formation with reaction/population interaction diffusion mechanisms -- Animal coat patterns and other practical applications of reaction diffusion mechanisms -- Neural models of pattern formation -- Mechanical models for generating pattern and form in development -- Evolution and developmental programmes -- Epidemic models and the dynamics of infectious diseases -- Geographic spread of epidemics -- Appendix 1. Phase plane analysis -- Appendix 2. Routh-Hurwitz conditions, jury conditions, Descarte's rule of signs and Exact solutions of a cubic -- Appendix 3. Hopf bifurcation theorem and limit cycles -- Appendix 4. General results for the Laplacian Operator in bounded domains ER -