Phase Transitions and Julia Sets

Kapitel in diesem Buch

1. Frontmatter 1
2. Preface 5
3. List of Contributors 6
4. Contents 7
5. Introductory Remarks 9
6. Part I: Theory of the Lotka-Volterra Approach
7. Complicated dynamics in simple models of ecological systems 13
8. Permanence in Lotka-Volterra and Replicator Equations 23
9. Dynamical regression in complex systems-Ecological examples 35
10. Chain decomposition of growth functions and structure models of ecological systems 45
11. Continuous Lotka-Volterra models for evolution processes 55
12. The Maximum Principle for Replicator Equations 63
13. Bilinear and Hamilton Systems, Macrodynamics 72
14. Part II: Julia Sets and Strange Attractors
15. Phase Transitions and Julia Sets 81
16. Geometry of Attractors, some rigorous results 103
17. Part III: Dynamic Systems and Information Problems
18. Some problems of the parameter identification of strange attractors 114
19. Chaotic dynamics of Information Processing: The 'magic number seven plus-minus tuo'revisited 123
20. Information-theoretical- methods in the stochastic theory of open systems 133
21. Part IV: Application of the Lotka-Uolterra Approach and other iteraction structures
22. Lotka-Uolterra Statistical Mechanics in cell-membrane/ cell-metabolism systems 143
23. The influence of noise on an biochemical oscillator 152
24. Models for parasitic diseases 162
25. Spontaneous biological pattern formation in three dimensions - The morphogene prepattern theory of mitosis and cytokinesis 170
26. Existence of wave trains in reaction-diffusion systems 182
27. Modelling the spatial evolution of population and employment - The case of the United States 191
28. Part V: Poster Contributions
29. Qualitative analysis of Volterra Equations and its Riccati Transformation uith special regard to bifurcation behaviour 213
30. Robustness of the solution of stochastic Volterra differential equations 217
31. An attempt of a fuzzy approach to Volterra systems 220
32. Chaos in a Lotka-Volterra-System - A numerical study 224
33. Structuring and Evolution Processes 228
34. Investigation of World Energy consumption and World Population in terms of a Hyperlogistic Evolution Model 232
35. Chain structures in 1-st order differential equations 236
36. State Models - An appropriate tool for improving the efficiency of biotechnical processes 241
37. Imigrating and Emigrating organisms in a Finite Volterra World 245
38. Discretness in a continous model of biological evolution 248
39. Dissipative structures in an ionic Lotka-Volterra type chemical reaction system 252
40. Effect of fluctuations on front propagation in nonequilibrium systems 258
41. Late Paper
42. The evolon growth model and its application to natural processes 261