... J. A. , 1985 , “ Determining Lyapunov Exponents From a Time Series ,” Physica D , 16 ( 3 ), pp. 285 – 317 . 10.1016/0167-2789(85)90011-9 16 05 2011 24 10 2011 25 10 2011 10 01 2012 10 01 2012 Lyapunov methods Poincare mapping roofs shapes (structures...

... chaos Lyapunov methods nonlinear dynamical systems Recently, stabilization of fractional-order chaotic systems has become a hot topic among scholars. In Ref. [ 22 ], based on the Takagi-Sugeno fuzzy model and impulsive control, some sufficient conditions have been presented to stabilize...

... 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...

..., Dynamical Systems, and Bifurcations of Vector Fields , Springer-Verlag , New York . 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...

... 2009 Chebyshev approximation control system synthesis large-scale systems linear systems Lyapunov methods nonlinear control systems observers Generally speaking, it is not possible to obtain all system states of a complex dynamics system by using a direct measurement approach...

... , “ Periodic, Quasiperiodic and Chaotic Behavior of a Driven Froude Pendulum ,” Int. J. Non-Linear Mech. 0020-7462 , 33 ( 6 ), pp. 947 – 965 . 22 02 2007 20 06 2007 12 11 2007 chaos differential equations Lyapunov methods nonlinear dynamical systems periodicity ratio...

... 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...

... phase space methods combinatorial mathematics mesh generation computational complexity discrete systems Lyapunov methods chain recurrence Lyapunov function Conley’s decomposition theorem algorithms computation combinatorial dynamics Identifying recurrent behavior...