complex systems physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno...

33
Complex Systems Physics

Upload: others

Post on 22-Mar-2021

2 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Complex Systems Physics

Page 2: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Emergence Phenomenon

Page 3: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Complex Interaction Networks

Page 4: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Epidemic Model for Covid-19

Page 5: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Epidemic Model for Covid-19

Page 6: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Adaptive Behaviour

Page 7: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

New Phase Transitions

Page 8: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Fitness Potential landscape

Page 9: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Fitness evolutionBacteria populations

Page 10: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Resilience of Ecosystems

Page 11: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Panic Phenomenon

Page 12: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Decision Mechanism

Page 13: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Double well emergent behavior

Page 14: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Chaotic behavior

Page 15: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Intermittency

Page 16: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Kicked pendulum: standard map

Hamiltonian dynamics Dissipative dynamics

Page 17: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Attractors

dissipativeStandard Map

Page 18: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Non Linear Dynamical Systems: Van der Poloscillator

Page 19: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Strange Attractors

Page 20: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Neuron model: bifurcation

Page 21: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Neuron Model

Page 22: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Heartbeat model

Page 23: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Arnold’s Cat Map

Page 24: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Hyperbolic maps

2x(mod1)

3x(mod1)

Page 25: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Random Walks

Page 26: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Statistical properties of RW

average variance

Page 27: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Average distance

Page 28: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Non Homogeneous random walk with zero mean value

Page 29: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Therophoresis model: random walk

Page 30: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Therophoresis model: distribution

X

Page 31: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Earthquake energy distribution

Page 32: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Avalanche dimension distribution

Page 33: Complex Systems Physics - unibo.it...1 oooo 0 20 40 60 100 120 140 160 180200 720 giorno (dall'I/I/2020) ... Simple Self-Organized Local Relationships . 1.6 1.2 100 1000 Time (generations)

Sentimental model