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Hidden attractor
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<p>In the <a href="/facts/Bifurcation_theory/sLsN54Rn">bifurcation theory</a>, a bounded <a href="/facts/Oscillation/6vSrm84a">oscillation</a> that is born without loss of stability of stationary set is called a hidden oscillation. In <a href="/facts/Nonlinear_control/KScKca1A">nonlinear control</a> theory, the birth of a hidden oscillation in a time-invariant control system with bounded states means crossing a boundary, in the domain of the parameters, where local stability of the stationary states implies global stability (see, e.g. <a href="/facts/Kalman%27s_conjecture/Nw7cF7XC">Kalman's conjecture</a>). If a hidden oscillation (or a set of such hidden oscillations filling a compact subset of the <a href="/facts/Phase_space/qPe4Fq57">phase space</a> of the <a href="/facts/Dynamical_system/782gREl5">dynamical system</a>) attracts all nearby oscillations, then it is called a hidden attractor. For a <a href="/facts/Dynamical_system/782gREl5">dynamical system</a> with a unique equilibrium point that is globally attractive, the birth of a hidden attractor corresponds to a qualitative change in behaviour from monostability to bi-stability. In the general case, a dynamical system may turn out to be <a href="/facts/Multistability/EqTGAqDW">multistable</a> and have coexisting local <a href="/facts/Attractor/FAx5Db4w">attractors</a> in the phase space. While trivial attractors, i.e. <a href="/facts/Attractor/FAx5Db4w">stable equilibrium points</a>, can be easily found analytically or numerically, the search of <a href="/facts/Limit_cycle/LmM9EVoA">periodic</a> and <a href="/facts/Chaos_theory/LTC17vsF">chaotic</a> attractors can turn out to be a challenging problem (see, e.g. <a href="/facts/Hilbert%27s_sixteenth_problem/SUR6JBKB">the second part of Hilbert's 16th problem</a>). </p>