Category:Dynamical systems

From Scholarpedia

A Dynamical system in mathematics is a system whose state in any moment of time is a function of its state in the previous moment of time and the input. Dynamical systems, in the form of ordinary differential equations of discrete mappings, describe most physical, chemical, and biological phenomena. Dynamical systems theory studies the solutions of such equations and mappings and their dependence on the initial conditions and the parameters.

See Dynamical Systems.

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Subcategories

There are 15 subcategories to this category.

B Bifurcations C Cardiac Dynamics Celestial mechanics Chaos Complexity

C cont. Computational Astrophysics Computational neuroscience D Differential Equations E Ergodic Theory H Hyperbolic Dynamics M Mappings

M cont. Morphogenesis N Numerical Analysis O Oscillators P Pattern Formation

Articles in category "Dynamical_systems"

There are 185 articles in this category.

1 1/f noise A ABC flow Ablowitz-Ladik equation Accretion discs Agent based modeling Agent-based computational economics Andrey Nikolaevich Kolmogorov Arnold cat map Artin-Mazur theorem Asymptotic cycles Attractor Attractor dimensions Attractor reconstruction Aubry-Mather theory Averaging Axiom A systems B Backward differentiation formulas Barkley model Basin of attraction Bautin bifurcation Belousov-Zhabotinsky reaction Bifurcation Biological fluid dynamics Blue-sky catastrophe Bogdanov-Takens bifurcation Boundary value problem Bowen-Margulis measure Brown dwarfs Bubbling transition Burst synchronization Bursting Butterfly effect C Canards Cellular neural network Center manifold Chain recurrent set Chaos Chaos in lasers Chaos in optics Chaos topology Chaotic advection Chaotic hypothesis Chaotic oscillators Chetaev function Chirikov criterion Chua circuit Coherence resonance Collisionless shock wave Combinatorial dynamics Complex systems Complexity Computational astrophysics Computational celestial mechanics Conductance-based models Conjugate maps Conley index Contraction theory Control theory Controlling chaos Core-collapse supernova simulations Crises

C cont. Cusp bifurcation D Decay of correlations Delay partial differential equations Delay-differential equations Delayed loss of stability Differential inclusions Differential-algebraic equations Distributional chaos Drift of spiral waves Duffing oscillator Dynamical billiards Dynamical systems E Encyclopedia of computational neuroscience Encyclopedia of dynamical systems Entropy Equation-free modeling Equilibrium Equivariant bifurcation theory Equivariant dynamical systems Ergodic theory Eta carinae Evans function F Fillipov (sliding) systems First passage time FitzHugh-Nagumo model Fixed point Flow curvature method Fluctuation theorem Fluctuations Fluid dynamics of swimming and flying Flux transport dynamos Fold-Hopf bifurcation Formal reaction kinetics Fractional differential equations Freeman's mass action G Galactic magnetic fields Game of life General linear methods Gierer-Meinhardt model Glassy dynamics Global bifurcations Grassberger-Procaccia algorithm H Haken-Kelso-Bunz model Hamilton-Jacobi equation Hamiltonian normal forms Hamiltonian systems Henri Poincaré Heteroclinic bifurcation Heteroclinic cycles Hilbert-Huang transform History of dynamical systems Holomorphic motions Homoclinic bifurcation Homoclinic orbit Homoclinic tangencies Homoclinic time reversible system Hopf-Hopf bifurcation Hydromagnetic dynamo theory Hyperbolic dynamics I Ikeda map Initial value problems Initiation of excitation waves

I cont. Integro-differential equations Invariant measure Isochron Iterated map Ito calculus J Jakobson theorem K Kadomtsev-Petviashvili equation Knot theory in flows Kolmogorov-Arnold-Moser theory Kolmogorov-Sinai entropy Kuramoto-Sivashinsky equation L Law of series Limit cycles of planar polynomial vector fields Lin's method Linear and nonlinear waves Local bifurcations of limit cycles Lorenz attractor Lozi map Lyapunov-Schmidt reduction M MATCONT MATLAB MHD reconnection Mackey-Glass equation Magneto-convection Magnetohydrodynamics Magnetorotational instability Maps with vanishing denominators Mathematical biology Meander of spiral waves Mechanoreceptors and stochastic resonance Method of lines Models of calcium dynamics Modern predator-prey models Morphogenesis Morris-Lecar model Morse-Smale systems Multi-stability in neuronal models Multiple scale analysis Multivariable control N Neimark-Sacker bifurcation Neural fields Neuronal avalanche Neuronal noise Neuronal synchrony measures Neuropercolation Neutral delay equations Non-uniformly hyperbolic attractors Noninvertibility Noninvertible maps Nonlinear Schrodinger systems: continuous and discrete Nonsmooth dynamical system Nonuniform hyperbolicity Normal forms Normal hyperbolicity O Optimal control Ordinary differential equations Oregonator Ornstein theory Oscillation death Oseledets theorem P Partial differential equation Partial hyperbolicity