Credits: 4 (3-1-0)
Prerequisites: PYL127 & PYL121 OR PYL551 & PYL553
Overlaps with: APL340, ESL300, AML836
Description
Introduction, phase space, stability analysis, bifurcations, iterative maps. Dissipative Systems; noninvertible maps; period-doubling and universality, intermittency.
Hamiltonian Systems; Integrability, Liouville’s theorem, action-angle variables, perturbation techniques, KAM theorem, area-preserving maps.
Fractals; Self-similarity; fractal dimensions and multifractals.
Chaos in plasmas, Generalised hydrodynamic model for strongly coupled plasma medium, connections with visco-elastic and soft matter.
Soft and Active matter: Nonlinear Rheology, Rhea-chaos, Oscillatory Chemical Reactions) Wrinkling, Folding.
Quantum chaos: Regular versus irregular states. Path Integrals. Random Matrix theory. Streamline and turbulent flows and transport for hydrodynamic and Magnetofluids, Kolmogorov’s 5/3 law.
Synchrony and phase transitions - Kuramoto model. Chaotic synchronization; the synchronization manifold.
Prerequisite Tree
flowchart TD
PYL711-1486[PYL711]
PYL711-1486 --- Or1487[Any one of]:::empty
Or1487 -.- and1488[ ]:::trueEmpty
and1488 --> PYL127-1488[PYL127]
and1488 --> PYL121-1488[PYL121]
Or1487 -.- and1489[ ]:::trueEmpty
and1489 --> PYL553-1489[PYL553]
and1489 --> PYL551-1489[PYL551]
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