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searching for Normal form (dynamical systems) 23 found (27 total)

alternate case: normal form (dynamical systems)

Floquet theory (1,315 words) [view diff] no match in snippet view article find links to article

unstable otherwise. Floquet theory is very important for the study of dynamical systems, such as the Mathieu equation. Floquet theory shows stability in Hill

Isochron (823 words) [view diff] no match in snippet view article find links to article

of dynamical systems, Physica D, 85:126–141 (1995) A.J. Roberts, Normal form transforms separate slow and fast modes in stochastic dynamical systems, Physica

Saddle-node bifurcation (805 words) [view diff] no match in snippet view article find links to article

bifurcation' is most often used in reference to continuous dynamical systems. In discrete dynamical systems, the same bifurcation is often instead called a fold

Jordan matrix (2,805 words) [view diff] no match in snippet view article find links to article

Many aspects of bifurcation theory for both continuous and discrete dynamical systems can be interpreted with the analysis of functional Jordan matrices

Pitchfork bifurcation (506 words) [view diff] no match in snippet view article find links to article

continuous dynamical systems described by ODEs—i.e. flows—pitchfork bifurcations occur generically in systems with symmetry. The normal form of the supercritical

Slow manifold (1,858 words) [view diff] no match in snippet view article find links to article

example of a center manifold. One of the main methods of simplifying dynamical systems, is to reduce the dimension of the system to that of the slow manifold—center

Hopf bifurcation (4,904 words) [view diff] no match in snippet view article find links to article

In the mathematics of dynamical systems and differential equations, a Hopf bifurcation is said to occur when varying a parameter of the system causes

Classification theorem (650 words) [view diff] no match in snippet view article find links to article

abstract algebra Jordan normal form – Form of a matrix indicating its eigenvalues and their algebraic multiplicities Frobenius normal form – Canonical form of

Stability theory (2,934 words) [view diff] no match in snippet view article find links to article

stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation

Center manifold (2,574 words) [view diff] no match in snippet view article find links to article

distinguishes Saturn's rings from a physical center manifold. Like most dynamical systems, particles in the rings are governed by second-order laws. Understanding

Marginal stability (1,001 words) [view diff] no match in snippet view article find links to article

In the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor

Paul Glendinning (550 words) [view diff] no match in snippet view article find links to article

(2014). "The Border Collision Normal Form with Stochastic Switching Surface" (PDF). SIAM Journal on Applied Dynamical Systems. 13: 181–193. doi:10.1137/130931643

List of chaotic maps (1,704 words) [view diff] no match in snippet view article find links to article

form of iterated functions. Chaotic maps often occur in the study of dynamical systems. Chaotic maps and iterated functions often generate fractals. Some

Thomas Kappeler (543 words) [view diff] no match in snippet view article find links to article

research was in global analysis, partial differential equations and dynamical systems in infinite dimensions. Kappeler co-founded the Zurich Graduate School

Stellar pulsation (3,258 words) [view diff] no match in snippet view article find links to article

Bibcode:1984ApJ...279..394B. doi:10.1086/161900. Buchler, J. R. (1993). "A Dynamical Systems Approach to Nonlinear Stellar Pulsations". Astrophysics and Space

List of undecidable problems (1,586 words) [view diff] no match in snippet view article find links to article

Moore, Cristopher (1990), "Unpredictability and undecidability in dynamical systems" (PDF), Physical Review Letters, 64 (20): 2354–2357, Bibcode:1990PhRvL

Perron–Frobenius theorem (8,215 words) [view diff] no match in snippet view article find links to article

probability theory (ergodicity of Markov chains); to the theory of dynamical systems (subshifts of finite type); to economics (Okishio's theorem, Hawkins–Simon

Immanuel Bomze (743 words) [view diff] no match in snippet view article find links to article

are in the areas of nonlinear optimization, qualitative theory of dynamical systems, game theory, mathematical modeling and statistics, where he has edited

Differential algebra (7,852 words) [view diff] no match in snippet view article find links to article

differential-algebraic system of equations. In a study of non-linear dynamical systems with chaos, researchers used differential elimination to reduce differential

Homology (mathematics) (8,273 words) [view diff] no match in snippet view article

network topology to evaluate, for instance, holes in coverage. In dynamical systems theory in physics, Poincaré was one of the first to consider the interplay

Artificial neuron (3,602 words) [view diff] no match in snippet view article find links to article

conjunctive normal form. Researchers also soon realized that cyclic networks, with feedbacks through neurons, could define dynamical systems with memory

Miroslav Krstić (5,194 words) [view diff] no match in snippet view article find links to article

covariance. EXTREMUM SEEKING. Krstić pioneered, for general nonlinear dynamical systems, extremum seeking (ES) as an approach for real-time model-free optimization

Markov chain (12,900 words) [view diff] no match in snippet view article find links to article

adjacency matrix can then provide a measure on the subshift. Many chaotic dynamical systems are isomorphic to topological Markov chains; examples include diffeomorphisms