Chaotic dynamics and fluctuations in a biochemical system

Chapters in this book

1. Frontmatter 1
2. Introductory Remarks 5
3. List of Participants 6
4. Contents 7
5. Part I: Mathematical Theory of Dynamical Systems
6. Hausdorff dimension of attractors: An example 9
7. K-stability as an ecologically more relevant stability concept 14
8. Stability, periodicity and chaos from the statistical point of view 24
9. Singularly perturbed autonomous differential systems 32
10. Difference equations with continuous time as mathematical models of the structure emergencies 40
11. Stability of equilibria in critical cases 50
12. Part II: General Mathematical Models
13. Permanence in population dynamics 58
14. Models of evolution processes including age structure 67
15. Pattern formation in an ionic reaction-diffusion system: A contribution to the morphogene prepattern theory of mitosis 76
16. Chaotic dynamics and fluctuations in a biochemical system 85
17. Periodic, quasiperiodic and chaotic motion in a forced predator-prey ecosystem 95
18. Chaotic dynamics of logical paradoxes 105
19. Control of growth processes 114
20. Part III. Mathematical Models for Concrete Processes
21. The Belousov-Zhabotinskii Reaction : A paradigm for theoretical studies of dynamical systems 122
22. The nitrogen transformation cycle in water 132
23. Modelling of polymer growth 139
24. A mathematical model of group defence in predator-prey systems 149
25. Vector-transmitted diseases in structured populations 154
26. Nonlinear behaviour in mathematical models of anaerobic digesters 162
27. Examples of computer-aided exploration and design of dynamical systems in neurosciences: Design of optimal nets 172
28. A dynamical model of synaptic transmission 182
29. Gradients for replicator systems 186
30. Part IV: Mathematical Description of Environmental Processes
31. The limiting factor concept in relation to stability, sensitivity and bifurcation in plankton models 196
32. Effects of structured environment to dynamic, behaviour : Some illustrations 209
33. Modelling and control of yeast growth in biotechnical systems 213
34. A dynamic simulation model of tree development under pollution stress 220
35. A biota model to assess the influence of human impacts on the global carbon cycle 230
36. An integrative approach to the solution of ecological problems with particular attention to the regional case 240
37. Application of the evolon model on evolution and energy growth processes 253
38. Non-linear dynamics of the epidemics of some childhood deseases in Copenhagen, Denmark 265
39. Modelling an estimating transport and fate of heavy metals in water column and sediment layer in some enclosed branches of the sea in the S.W. Netherlands 273
40. POSTER SESSION
41. Mathematical software developed by the Karl-Weierstraß-Institute of Mathematics 282