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A lyapunov function is a scalar function defined on the phase space, which can be used to prove the stability of an equilibrium point.
Estimates for investigates global attractors and invariant sets for dynamical systems by means of lyapunov functions and adapted metrics.
Pullback attractors of non-autonomous dynamical systems in banach spaces with morse decomposition, attractor, repeller, morse set, lyapunov function,.
The potential function includes also some significant characteristics of the attractors of the system, such as oscillatory and stability etc - this is also because they.
Defined by the partial differential equation for the function y(x, t) λ1 denotes the largest lyapunov exponent.
Oct 3, 2019 under the assumption of uniform asymptotic stability of λ in the sense of lyapunov, we show that discretized versions of the dynamical system.
The theory of attractors plays an important role in the study of the asymptotic behaviors of dynamical systems.
Keywords: stability, capsize, lyapunov, attractor, lorenz elongation of ellipse axes as an exponential function of lyapunov exponents.
Leonov, lyapunov functions in the attractors dimension theory, journal of applied mathematics and mechanics 76 (2) (2012) 129–141.
3 that a global bifurcation plays a key role in the formation of the lorenz attractor. So the lyapunov function is strictly decreasing for all values (x(t), y(t), z(t)).
Abstract we investigate additional regularity properties of all globally defined weak solutions, their global and trajectory attractors for classes of semi-linear.
Initial conditions lie indeed in the basins of attraction of the corresponding attractors. In order to estimate basins of attraction, lyapunov functions can be used.
Keywords: compact metric space; global attractor; lyapunov function; set-valued mapping; turnpike.
For attractors smoothness of the lyapunov function has not been an issue. Charles conley has generalized the theory to include isolated blocks.
Nov 13, 2017 basin of attraction using a lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, israel-stewart.
Feb 5, 2019 dynamical systems and chaos: lyapunov exponents (optional) topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation.
Nov 13, 2017 the non-equilibrium attractors of systems undergoing gubser flow within and characterizing the basin of attraction using a lyapunov function.
Jan 7, 2020 the equatorial ring configures to be as a stable attractor and the whole we propose three different lyapunov functions, each one carrying.
Jul 30, 2020 our approach uses (generalised) lyapunov functions to find attracting sets, which must contain the global attractor, and the choice of lyapunov.
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