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Decoupling normalizing transformations and local stabilization of nonlinear systems

S. Nikitin (1996)

Mathematica Bohemica

The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.

Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions

Szabolcs Rozgonyi, Katalin M. Hangos, Gábor Szederkényi (2010)


In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions V n in a rational functional form approximating a maximal Lyapunov function V M that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions V n for a class of hybrid (piecewise...

Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems

Song Zheng (2020)


This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed systems,...

Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium

Rogério Martins, Gonçalo Morais (2015)


An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented...

Impulsive stabilization and synchronization of uncertain financial hyperchaotic systems

Song Zheng (2016)


In this paper the issue of impulsive stabilization and synchronization of uncertain financial hyperchaotic systems with parameters perturbation is investigated. Applying the impulsive control theory, some less conservative and easily verified criteria for the stabilization and synchronization of financial hyperchaotic systems are derived. The control gains and impulsive intervals can be variable. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse...

Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics

T. Stiehl, A. Marciniak-Czochra (2012)

Mathematical Modelling of Natural Phenomena

The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts....

Modifying some foliated dynamical systems to guide their trajectories to specified sub-manifolds

Prabhakar G. Vaidya, Swarnali Majumder (2011)

Mathematica Bohemica

We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate...

Stability analysis of uncertain complex-variable delayed nonlinear systems via intermittent control with multiple switched periods

Song Zheng (2018)


In this paper, an intermittent control approach with multiple switched periods is proposed for the robust exponential stabilization of uncertain complex-variable delayed nonlinear systems with parameters perturbation, in which the considered complex systems have bounded parametric uncertainties. Based on the Lyapunov stability theory and comparison theorem of differential equations, some stability criteria are established for a class of uncertain complex delayed nonlinear systems with parameters...

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