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Continuous separation for monotone skew-product semiflows: From theoretical to numerical results

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  • This paper investigates relevant dynamical properties of nonautonomous linear cooperative families of ODEs and FDEs based on the existence of a continuous separation. It provides numerical algorithms for the computation of the dominant one-dimensional subbundle of the continuous separation and the upper Lyapunov exponent of the semiflow. The extension of the theory to general linear cooperative families of ODEs and FDEs without strong monotonicity is also given. Finally these methods and results are applied in the study of nonlinear families of neural networks of Hopfield type with sigmoidal activation function.
    Mathematics Subject Classification: 37C60, 37C65, 37M25, 37B05.


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