Presentation is loading. Please wait.

Presentation is loading. Please wait.

Published by Modified over 9 years ago

Similar presentations

Presentation on theme: ""— Presentation transcript:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48 saddle limit cycle unstable equilibria stable limit cycle separatrix chaotic attractor M.P. Boer The dynamics of tritrophic food chains Vrije Universiteit Amsterdam (2000) prey predator top-predator

49 M.P. Boer The dynamics of tritrophic food chains Vrije Universiteit Amsterdam (2000) saddle limit cycle homoclinic- connection unstable equilibria stable limit cycle prey predator top-predator

50 M.P. Boer The dynamics of tritrophic food chains Vrije Universiteit Amsterdam (2000) saddle limit cycle heteroclinic- connection unstable equilibria stable limit cycle prey predator top-predator

51

52

Download ppt ""

Similar presentations

Game Dynamics Econ 171. Two Population Games A Predator Why Does He Need to be so fast?

Game Dynamics Econ 171. Two Population Games A Predator Why Does He Need to be so fast?
Hamiltonian Chaos and the standard map Poincare section and twist maps. Area preserving mappings. Standard map as time sections of kicked oscillator (link.

Hamiltonian Chaos and the standard map Poincare section and twist maps. Area preserving mappings. Standard map as time sections of kicked oscillator (link.
What’s a food chain? Predators and prey Food Chains.

What’s a food chain? Predators and prey Food Chains.
Pond Dynamics and Balance. Water Quality Factors 1. Dissolved oxygen 2. Alkalinity 3. Hardness 4. pH.

Pond Dynamics and Balance. Water Quality Factors 1. Dissolved oxygen 2. Alkalinity 3. Hardness 4. pH.
1 Ecological implications of global bifurcations George van Voorn 17 July 2009, Oldenburg For the occasion of the promotion of.

1 Ecological implications of global bifurcations George van Voorn 17 July 2009, Oldenburg For the occasion of the promotion of.
Arshak Grigoryan Project for Math. Modeling. Predator-Prey model (By Odell) Lets consider one of the variations of the Odell`s model where x, y are population.

Arshak Grigoryan Project for Math. Modeling. Predator-Prey model (By Odell) Lets consider one of the variations of the Odell`s model where x, y are population.
Many decades, huge area – spatially and temporally extensive cycling.

Many decades, huge area – spatially and temporally extensive cycling.
WINNERLESS COMPETITION PRINCIPLE IN NEUROSCIENCE Mikhail Rabinovich INLS University of California, San Diego ’

WINNERLESS COMPETITION PRINCIPLE IN NEUROSCIENCE Mikhail Rabinovich INLS University of California, San Diego ’
Ecological consequences of global bifurcations

Ecological consequences of global bifurcations
3-D State Space & Chaos Fixed Points, Limit Cycles, Poincare Sections Routes to Chaos –Period Doubling –Quasi-Periodicity –Intermittency & Crises –Chaotic.

3-D State Space & Chaos Fixed Points, Limit Cycles, Poincare Sections Routes to Chaos –Period Doubling –Quasi-Periodicity –Intermittency & Crises –Chaotic.
General strong stabilisation criteria for food chain models George van Voorn, Thilo Gross, Bob Kooi, Ulrike Feudel, Bas Kooijman

General strong stabilisation criteria for food chain models George van Voorn, Thilo Gross, Bob Kooi, Ulrike Feudel, Bas Kooijman
Continuation of global bifurcations using collocation technique George van Voorn 3 th March 2006 Schoorl In cooperation with: Bob Kooi, Yuri Kuznetsov.

Continuation of global bifurcations using collocation technique George van Voorn 3 th March 2006 Schoorl In cooperation with: Bob Kooi, Yuri Kuznetsov.
Mini-course bifurcation theory George van Voorn Part three: bifurcations of 2D systems.

Mini-course bifurcation theory George van Voorn Part three: bifurcations of 2D systems.
Mini-course bifurcation theory George van Voorn Part four: chaos.

Mini-course bifurcation theory George van Voorn Part four: chaos.
How do the basic reproduction ratio and the basic depression ratio determine the dynamics of a system with many host and many pathogen strains? Rachel.

How do the basic reproduction ratio and the basic depression ratio determine the dynamics of a system with many host and many pathogen strains? Rachel.
Mini-course bifurcation theory George van Voorn Part two: equilibria of 2D systems.

Mini-course bifurcation theory George van Voorn Part two: equilibria of 2D systems.
vrije Universiteit amsterdamPostacademische Cursus Informatie Technologie Web Applications Anton Eliëns Vrije Universiteit, Amsterdam 19 October 1999.

vrije Universiteit amsterdamPostacademische Cursus Informatie Technologie Web Applications Anton Eliëns Vrije Universiteit, Amsterdam 19 October 1999.
Lorenz system Stationary states: pitchfork bifurcation: r= 1

Lorenz system Stationary states: pitchfork bifurcation: r= 1
Epidemics on Attractors. Epidemics In Strongly Fluctuating Populations.

Epidemics on Attractors. Epidemics In Strongly Fluctuating Populations.
1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950 1.f has a saddle point at (1,1) 2.f has a local minimum at.

f has a saddle point at (1,1) 2.f has a local minimum at.

Similar presentations

Ads by Google