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In [[mathematics]], the concept of '''graph dynamical systems''' can be used to capture a wide range of processes taking place on graphs ...i Wah |year=2005 |title=Synchronization in networks of nonlinear dynamical systems coupled via a directed graph |journal=Nonlinearity |volume= 18 |issue= 3|pa ...

Suppose we start with a random trajectory and perturb it by a small amount, <math>\epsilon</math>, in a random direction. If the new trajectory ends up ...

{{short description|Network of coupled dynamical systems}} A '''synchronization network''' is a network of coupled [[dynamical systems]]. It consists of a network connecting oscillators, where oscillators are ...

...ricans|American]] [[mathematician]] who has done research into [[dynamical systems]] and the complexity of [[real number]] algorithms. ...In 1974, he proposed the Entropy Conjecture, an open problem in dynamical systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 198 ...

...d in each timestep each node <math>j</math> forms ties to <math> m </math> random other nodes at rate <math> a_i=\eta x_i</math> (more precisely, it does so ...<math> \langle a^2\rangle</math>) are the first and second moments of the random activity-rate <math> a_j</math>. ...

...punov]], describe characteristic expanding and contracting directions of a dynamical system. They have been used in predictability analysis and as initial pertu Lyapunov vectors are defined along the trajectories of a dynamical system. If the system can be described by a d-dimensional state vector <mat ...

...nics and in 2002 the head of the Department of Mathematical Statistics and Random Processes. At the [[Steklov Institute of Mathematics]] he became in 2003 he ...l equations and topological considerations in the integrability of dynamic systems. In 1979 he proved that for 2-dimensional manifolds <math>M</math> with gen ...

...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&md Consider the [[dynamical system]] ...

...CCM is based on the theory of [[dynamical system]]s and can be applied to systems where causal variables have synergistic effects. As such, CCM is specifical ...applied. Takens' theorem generically proves that the [[state space]] of a dynamical system can be reconstructed from a single observed time series of the syste ...

...a model''' (rGLV) is an [[ecological model]] and [[Random dynamical system|random set of coupled ordinary differential equations]] where the parameters of th ...tle=Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka–Volterra model of ecosystems |url=https://iopscie ...

...Sitnikov problem ideal for general studies on effects in chaotic dynamical systems. ...original Sitnikov article – new insights''. In: ''Celestial Mechanics and Dynamical Astronomy'', 56/1993, pp.&nbsp;99–101, {{ISSN|0923-2958}}, [http://adsabs.h ...

...ory''' is an area of mathematics that studies the evolution of [[dynamical systems]] under constraints on the system [[state space (controls)|state]].<ref>{{c ...in a stochastic way. Rather they evolve with a Darwinian flavor, driven by random fluctuations but yet constrained to remain "viable" by their environment. V ...

...fiber-wise proofs for center foliations of partially hyperbolic dynamical systems: these foliations are typically Hölder but not absolutely continuous. A dynamical version for center foliation was constructed by [[Amie Wilkinson]] and [[Mi ...

....T. |date= 2003 |title=Constructive effects of noise in homoclinic chaotic systems |journal= Phys. Rev. E |volume=67 |issue= 6 |page= 066220 |doi=10.1103/Phys ...</ref> Matsumoto and Tsuda introduced a one-dimensional model, a [[random dynamical system]] with uniform additive noise, driven by the map: ...

...lar automata''' or '''probabilistic cellular automata''' ('''PCA''') or '''random cellular automata''' or '''locally interacting [[Markov chain]]s'''<ref>{{c | title = Locally Interacting Systems and their Application in Biology: Proceedings of the School-Seminar on Mark ...

...oncerned with the long term behavior of the solutions of [[dissipative]] [[dynamical system]]s. Inertial manifolds are finite-dimensional, smooth, [[invariant ...A. J. | title=Simple examples of the derivation of amplitude equations for systems of equations possessing bifurcations | journal=Journal of the Australian Ma ...

...pg|300px|thumbnail|right|Time series of Rulkov map showing three different dynamical regimes]] ...ional advantages because the map is easier to iterate than a [[continuous dynamical system]]. This saves memory and simplifies the computation of large neural ...

| title = Topics in Thermodynamic Formalism: Random Equilibrium States and Ergodic Optimisation | journal = Discrete and Continuous Dynamical Systems ...

...in several equivalent ways, describing alternative ways of performing this random shuffle: ...come from the first or the second packet.<ref name="bd92"/> To generate a random permutation according to this model, begin by flipping a [[fair coin]] <mat ...

...014-4423}}</ref><ref>Ross et al, Unscented Control for Uncertain Dynamical Systems, US Patent US 9,727,034 Bl. Issued Aug 8, 2017. ...015|title=Riemann-Stieltjes Optimal Control Problems for Uncertain Dynamic Systems|url=https://doi.org/10.2514/1.G000505|journal=Journal of Guidance, Control, ...