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Global asymptotic stability for plane polynomial flows [PDF]
Časopis pro pěstování matematiky, 1986 The authors consider a two-dimensional system of ODE and, using a theorem regarding stability of polynomial flows, prove that if the trace of the Jacobian matrix is negative and its determinant is positive, then the asymptotic stability is assured.
Meisters, Gary H., Olech, Czesław
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Global asymptotic stability of solutions of cubic stochastic difference equations
Advances in Difference Equations, 2004 Global almost sure asymptotic stability of solutions of some nonlinear stochastic difference equations with cubic-type main part in their drift and diffusive part driven by square-integrable martingale differences is proven under appropriate conditions ...
Henri Schurz, Alexandra Rodkina
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Global stability of a predator-prey model with Beddington–DeAngelis and Tanner functional response
Electronic Journal of Qualitative Theory of Differential Equations, 2017 In this paper, we study the global stability of a predator–prey system with Beddington–DeAngelis and Tanner functional response. By using the iteration method and comparison principle, we prove the global asymptotic stability of the unique positive ...
Nai-Wei Liu, Na Li
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Global Asymptotic Stability in Some Discrete Dynamical Systems
Journal of Mathematical Analysis and Applications, 1999 The paper deals with the stability of the equilibrium of a discrete dynamical system \(x_{n+1}=Tx_n\) in a metric space \((M,d)\). Under some natural conditions the authors show that the unique equilibrium is globally asymptotically stable. Taking for \(d\) the part-metric, the authors obtain the strong negative feedback property as a special case ...
Kruse, Nicole, Nesemann, Tim
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Mathematics, 2020 In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved.
Andrey Zahariev, Hristo Kiskinov
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Uniform Asymptotic Stability and Global Asymptotic Stability for Time-Delay Hopfield Neural Networks [PDF]
, 2012 In this paper, we consider the uniform asymptotic stability and global asymptotic stability of the equilibrium point for time-delays Hopfield neural networks. Some new criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov ...
Arbi, Adnene +2 more
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Mathematics, 2020 We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper.
Usa Humphries +6 more
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Global asymptotic stability of a nonlinear recursive sequence
Applied Mathematics Letters, 2004 Using a ``semicycle analysis method'' developed by the authors, they prove that the positive equilibrium of the nonlinear difference equation \[ x_{n+1}=\frac{x_nx_{n-1}^b+x_{n-2}^b+a}{x_{n-1}^b+x_nx_{n-2}^b+a}, \quad n\geq 0 \] is globally asymptotically stable for parameters \(a\geq 0\), \(b>0\) and initial values \(x_{-2},x_{-1},x_0>0\).
Xianyi, Li, Zhu, Deming
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On the Stability of Some Discrete Fractional Nonautonomous Systems
Abstract and Applied Analysis, 2012 Using the Lyapunov direct method, the stability of discrete nonautonomous systems within the frame of the Caputo fractional difference is studied. The conditions for uniform stability, uniform asymptotic stability, and uniform global stability are ...
Fahd Jarad +3 more
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Stability of the third order rational difference equation
MANAS: Journal of Engineering, 2020 In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\]where the initial conditions are non zero real numbers and are ...
Mehmet Emre Erdoğan
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