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Non-Linear Dynamics

Published on Apr 03, 20171704 Views

Colm Connaughton

For many non-specialists, notions of nonlinearity, chaos and complexity are often blurred together in scientific discourse. In reality, chaos is only one of a rich set of important phenomena observed

Winter School on Complexity Science 2017 - Singapore

Related categories

PhysicsComplexity ScienceComputer ScienceData ScienceMathematics

Chapter list

Nonlinear dynamics00:00
Outline02:04
What is nonlinearity?04:54
What is dynamics?06:42
Turbulence: Complicated nonlinear equations can have complicated solutions08:26
Chaos: Simple nonlinear equations can have complicated solutions09:58
Nonlinear dynamics and chaos11:56
Nonlinear dynamics and complexity science20:51
Fixed points25:51
Stable and unstable fixed points25:59
Phase space, trajectories and parameters28:23
Invariant sets and attractors28:49
Bifurcations29:16
Types of bifurcations 1: Saddle-node (or fold) bifurcation and tipping points31:28
Types of bifurcations 2: (Supercritical) pitchfork bifurcation and multistability37:03
Types of bifurcations 3: (Subcritical) pitchfork bifurcation43:07
Types of bifurcations 3: Stabilised subcritical pitchfork bifurcation and hysteresis44:33
Types of bifurcations 4: Hopf bifurcation and nonlinear oscillations47:49
Conclusions and summary51:22
http://www.warwick.ac.uk/go/mathsys52:23
http://lml.org.uk/events/summer-school/52:35
Practical example: Multistability in visual perception53:03