## Mathematical ecology and biology

** Allocation of 1998 classes is here**
### Synopsis

#### A. Stability

- Continuous population models: stability, bifurcations. [Drazin, 1.3-1.5.]
- Hysteresis, non-dimensionalisation.
- Discrete models: stability, chaos.
- Harvesting: optimal strategies.
#### B. Oscillations

- Lotka-Volterra model. [Jordan and Smith, 2.1-2.3.]
- Predator-prey systems.
- Limit cycles.
#### C. Enzyme reactions

- Michaelis-Menten kinetics: pseudo-steady state hypothesis.
- Allosteric enzymes.
- Glycolysis.
- Glycolytic oscillations.
#### D. Waves

- Fisher equation.
- Excitable media.
- Signal propagation in nerve cells.
#### E. Pattern formation

- Reaction-diffusion.
- Turing instability.

### Reading

- J.D. Murray, Mathematical biology. Springer-Verlag, 2nd ed., 1993.
- F. Hoppensteadt, Mathematical theories of populations: demographics,
genetics and
epidemics. SIAM, Philadelphia, 1975 (reprinted 1993).
- L.A. Segel, Modeling dynamic phenomena in molecular and cellular
biology. C.U.P.,
1984.
- S.I. Rubinow, Introduction to mathematical biology. John Wiley,
1975.
- A. Goldbeter, Biochemical oscillations and cellular rhythms. C.U.P.,
1996.
- E. Renshaw, Modelling biological populations in space and
time. C.U.P., 1991.

Also:
- P.G. Drazin, Nonlinear systems. C.U.P., 1992.
- D.W. Jordan and P. Smith, Nonlinear ordinary differential
equations, 2nd ed. O.U.P., 1987.

### Course materials

These can be downloaded as postscript files; currently available are