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Discretization of Second Lyapunov Method
Qualitative Theory of Dynamical Systems, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Polulyakh, Eugene +2 more
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Lyapunov based reasoning methods
IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2001Semiquantitative simulation is an approach for the analysis of uncertain dynamic systems that performs a comprehensive simulation study based on automated reasoning methods. Semiquantitative simulation of complex models is, however, hindered by the limited automated reasoning capabilities of the currently available semiquantitative simulation ...
M. Hofbauer, N. Dourdoumas
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Suppressing chaos via Lyapunov–Krasovskii’s method
Chaos, Solitons & Fractals, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuang, JL, Meehan, PA, Leung, AYT
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Parallelizable Flows and Lyapunov's Second Method
The Annals of Mathematics, 1961This paper is divided into two parts. Part I deals with flows on arbitrary metric spaces and answers completely the question when they are parallelizable. We give an elementary proof for arbitrary locally compact separable metric spaces which, incidentally, also clarifies the role of Niemytskii's notion of an improper saddle point.
Dugundji, John, Antosiewicz, H. A.
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Computing Lyapunov exponents of continuous dynamical systems: method of Lyapunov vectors
Chaos, Solitons & Fractals, 2005The paper proposes a new method for computing the Lyapunov characteristic exponents of general continuous dynamical systems. There are several methods for finding numerical values of Lyapunov's exponents, e.g., Wolf's algorithm and the QR method.
Lu, Jia +3 more
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Some Refinements of Lyapunov's Second Method
Canadian Journal of Mathematics, 1965Lyapunov's second method is a well-known and powerful tool for studying the behaviour of solutions of a system of differential equations. One approach to the theory is the comparison method developed by Corduneanu (4). This approach has the advantage that it also leads to other results on asymptotic behaviour which originally appeared to be unrelated ...
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Projection methods preserving Lyapunov functions
BIT Numerical Mathematics, 2010The authors propose explicit Runge-Kutta methods for the numerical solution of initial value problems for autonomous ordinary differential equations which have a known Lyapunov function. The integrators preserve this geometric quantity by proceeding as follows: First, one step of the Runge-Kutta method is performed.
Calvo, M. +3 more
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2020
The celebrated Lyapunov function method (or the direct Lyapunov method) introduced in the Ph.D. thesis of A. M. Lyapunov in 1892 is a simple effective tool for stability analysis of differential equations. The main advantage of this method lies in the fact that a decision on stability or instability can be made by means of a certain investigation of ...
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The celebrated Lyapunov function method (or the direct Lyapunov method) introduced in the Ph.D. thesis of A. M. Lyapunov in 1892 is a simple effective tool for stability analysis of differential equations. The main advantage of this method lies in the fact that a decision on stability or instability can be made by means of a certain investigation of ...
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1999
In Chapter 7 we discussed the first approach to realization of the Lyapunov direct method for FDE based on application of the Lyapunov functionals. In the second approach finite dimensional Lyapunov’s functions v(t, x): R × R n →R are used.
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In Chapter 7 we discussed the first approach to realization of the Lyapunov direct method for FDE based on application of the Lyapunov functionals. In the second approach finite dimensional Lyapunov’s functions v(t, x): R × R n →R are used.
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The Lyapunov–Razumikhin Method: CNNs
2013In this chapter, by using the concept of differential equations with piecewise constant arguments of generalized type [13–15, 18], the model of cellular neural networks (CNNs) [79, 80] is developed. Lyapunov–Razumikhin technique is applied to find sufficient conditions for uniform asymptotic stability of equilibria.
Marat Akhmet, Enes Yılmaz
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