Number of variables
Nonlinearity
n = 1
n = 2
n ≥ 3
n >> 1
Continuum
Linear
Growth, decay, or equilibrium
Exponential growth
RC circuit
Radioactive decay
Oscillations
Linear oscillator
Mass and spring
RLC circuit
2-body problem (Kepler, Newton)
Civil engineering, structures
Electrical engineering
Collective phenomena
Coupled harmonic oscillators
Solid-state physics
Molecular dynamics
Equilibrium statistical mechanics
Waves and patterns
Elasticity
Wave equations
Electromagnetism (Maxwell)
Quantum mechanics (Schrödinger, Heisenberg, Dirac)
Heat and diffusion
Acoustics
Viscous fluids
Nonlinear
Fixed points
Bifurcations
Overdamped systems, relaxational dynamics
Logistic equation for single species
Pendulum
Anharmonic oscillators
Limit cycles
Biological oscillators (neurons, heart cells)
Predator-prey cycles
Nonlinear electronics (van der Pol, Josephson)
The frontier
Chaos
Strange attractors (Lorenz)
3-body problem (Poincaré)
Chemical kinetics
Iterated maps (Feigenbaum)
Fractals (Mandelbrot)
Forced nonlinear oscillators (Levinson, Smale)
Practical uses of chaos
Quantum chaos ?
Coupled nonlinear oscillators
Lasers, nonlinear optics
Nonequilibrium statistical mechanics
Nonlinear solid-state physics (semiconductors)
Josephson arrays
Heart cell synchronization
Neural networks
Immune system
Ecosystems
Economics
Spatio-temporal complexity
Nonlinear waves (shocks, solitons)
Plasmas
Earthquakes
General relativity (Einstein)
Quantum field theory
Reaction-diffusion, biological and chemical waves
Fibrillation
Epilepsy
Turbulent fluids (Navier-Stokes)
Life
Extended Domains & Applications
Engineering & Control
Feedback control systems (PID controllers)
Multi-body dynamics (robotic manipulators)
Fluid–structure interaction systems
Power systems dynamics (electrical grids)
Biology & Neuroscience
Genetic regulatory networks
Cell signaling pathways (MAPK, calcium)
Neural population dynamics (Wilson–Cowan)
Epidemic models (SIR, SEIR)
Metabolic pathway dynamics
Social Sciences & Economics
Agent-based models (traffic flow, crowds)
Opinion dynamics (DeGroot, bounded confidence)
Market models (stock prices, macro cycles)
Food webs and ecological networks
Evolutionary games (replicator dynamics)
Mathematics & Computation
Cellular automata (Game of Life)
Delay differential equations
Stochastic differential equations
Fractional-order systems
Functional differential equations
Physics & Physical Chemistry
Turbulence models (RANS, LES, DNS)
Nonlinear optics (soliton propagation)
Spin systems (Ising, Heisenberg)
Complex fluids (non-Newtonian)
Plasma dynamics (Vlasov, MHD)
Reaction-diffusion systems (Turing patterns)
Quantum & Relativistic
Open quantum systems (Lindblad equation)
Many-body quantum dynamics (Hubbard model)
Bose–Einstein condensates
Quantum statistical mechanics
Relativistic fluid dynamics