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Generalized synchronization in the networks with directed acyclic structure

Sergej Čelikovský, Volodymyr Lynnyk, Anna Lynnyk, Branislav Rehák (2023)

Kybernetika

Generalized synchronization in the direct acyclic networks, i.e. the networks represented by the directed tree, is presented here. Network nodes consist of copies of the so-called generalized Lorenz system with possibly different parameters yet mutually structurally equivalent. The difference in parameters actually requires the generalized synchronization rather than the identical one. As the class of generalized Lorenz systems includes the well-known particular classes such as (classical) Lorenz...

Global asymptotic stability for half-linear differential systems with coefficients of indefinite sign

Jitsuro Sugie, Masakazu Onitsuka (2008)

Archivum Mathematicum

This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system x ' = - e ( t ) x + f ( t ) φ p * ( y ) , y ' = - g ( t ) φ p ( x ) - h ( t ) y , where p > 1 , p * > 1 ( 1 / p + 1 / p * = 1 ), and φ q ( z ) = | z | q - 2 z for q = p or q = p * . The coefficients are not assumed to be positive. This system includes the linear differential system 𝐱 ' = A ( t ) 𝐱 with A ( t ) being a 2 × 2 matrix as a special case. Our results are new even in the linear case ( p = p * = 2 ). Our results also answer the question whether the zero solution of the linear system is asymptotically stable even when Coppel’s condition does not hold...

Global attractor of a differentiable autonomous system on the plane

Nguyen Van Chau (1995)

Annales Polonici Mathematici

We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.

Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment

Bingwen Liu (2016)

Annales Polonici Mathematici

This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.

Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses

Ramalingam Sriraman, Asha Nedunchezhiyan (2022)

Kybernetika

In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the n -dimensional Clifford-valued neural network into 2 m n -dimensional real-valued counterparts in order to solve the noncommutativity...

Currently displaying 321 – 340 of 933