We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of Pk and prove that it is equivalent to the stability of repelling cycles or the existence of a measurable holomorphic motion of Julia sets. We characterize the corresponding bifurcations by the strict subharmonicity of the sum of Lyapunov exponents or the instability of critical dynamics and a...

Many processes in automatic regulation, physics, mechanics, biology, economy, ecology etc. can be modelled by hereditary systems (see, e.g. [1-3]). One of the main problems for the theory of such systems and their applications is connected with stability [1,2]. Many stability results were obtained by the construction of appropriate Lyapunov functionals. In [4-8] the method is proposed allowing,...

In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the presen...

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead ...

We consider the basic model of virus dynamics with noncytolytic loss of infected cells for the infection with viral hepatitis B. Stability of the infection-free steady state and existence, uniqueness and stability of the infected steady state is investigated. The stability results are given in terms of the basic reproductive number R0. Here, we perform the global stability analysis using two te...

This paper deals with the stability of continuous-time multidimensional nonlinear systems in the Roesser form. The concepts from 1D Lyapunov stability theory are first extended to 2D nonlinear systems and then to general continuous-time multidimensional nonlinear systems. To check the stability, a direct Lyapunov method is developed. While the direct Lyapunov method has been recently proposed f...

In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (or characteristic exponents) are negative, then the solution of the original system is asymptotically Lyapunov stable. In 1930, it was stated by O. Perron that the requirement of regularity of the firs...

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the inputto-state stability of a system. Then for the case of the systems described by abstract equations in Banach spaces we develop two methods of construction of local and global I...

This paper is concerned with fuzzy cellular neural networks with distributed delays. Sufficient conditions on the existence, uniqueness and global exponential stability of equilibrium point are established by using the Homeomorphism theory and applying elementary inequality 2ab ≤ a2 + b2. Moreover an example is given to illustrate results obtained. Key–Words: Fuzzy cellular neural networks, Glo...