... criteria and Lyapunov exponent evolution as quantitative criterion are used to investigate the emergence of chaotic response. 16 05 2011 24 10 2011 25 10 2011 10 01 2012 10 01 2012 Lyapunov methods Poincare mapping roofs shapes (structures) structural engineering tanks...

... control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time. 11 08 2011 13 10 2011 09 01 2012 09 01 2012 chaos Lyapunov methods nonlinear...

... trajectory, and then carry out the approximation of the Lyapunov exponents using techniques for linear problems. 27 05 2009 20 04 2010 27 09 2010 27 09 2010 approximation theory Jacobian matrices Lyapunov methods nonlinear differential equations vectors Lyapunov...

... bifurcations. 19 09 2008 22 04 2009 29 06 2010 29 06 2010 asymptotic stability bifurcation delays Lyapunov methods mathematical analysis neural nets neural networks delay differential equation bifurcation periodic oscillation multistability Over...

... is shown in Fig. 8 . States of the original system States of the error dynamics 28 01 2008 23 12 2008 19 05 2009 Chebyshev approximation control system synthesis large-scale systems linear systems Lyapunov methods nonlinear control systems observers...

.... 7 . 22 02 2007 20 06 2007 12 11 2007 chaos differential equations Lyapunov methods nonlinear dynamical systems periodicity ratio Lyapunov exponent irregular motions nonlinear dynamics nonlinear differential equations chaos periodic behavior quasiperiodic...

... motion control stability Lyapunov methods Chebyshev approximation polynomials iterative methods The operation of periodic mechanical systems depends, among other things, on two effects: the dissipation (damping) and the excitation. The dissipation is usually produced by friction...

... functions are weak Lyapunov functions and well-approximate a continuous Lyapunov function for the underlying map. phase space methods combinatorial mathematics mesh generation computational complexity discrete systems Lyapunov methods Proof. Let A be an attractor. Then F...