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Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations

A. U. Afuwape, Mathew Omonigho Omeike (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we shall give sufficient conditions for the ultimate boundedness of solutions for some system of third order non-linear ordinary differential equations of the form X w i d t h 0 p t h e i g h t 5 . 46 p t t o 8 p t . . . + F ( X ¨ ) + G ( X ˙ ) + H ( X ) = P ( t , X , X ˙ , X ¨ ) where X , F ( X ¨ ) , G ( X ˙ ) , H ( X ) , P ( t , X , X ˙ , X ¨ ) are real n -vectors with F , G , H : ℝ n → ℝ n and P : ℝ × ℝ n × ℝ n × ℝ n → ℝ n continuous in their respective arguments. We do not necessarily require that F ( X ¨ ) , G ( X ˙ ) and H ( X ) are differentiable. Using the basic tools of a complete Lyapunov Function, earlier results are generalized.

Generalized practical stability analysis of discontinuous dynamical systems

Guisheng Zhai, Anthony Michel (2004)

International Journal of Applied Mathematics and Computer Science

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 present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and...

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.

Growth conditions for the stability of a class of time-varying perturbed singular systems

Faten Ezzine, Mohamed Ali Hammami (2022)

Kybernetika

In this paper, we investigate the problem of stability of linear time-varying singular systems, which are transferable into a standard canonical form. Sufficient conditions on exponential stability and practical exponential stability of solutions of linear perturbed singular systems are obtained based on generalized Gronwall inequalities and Lyapunov techniques. Moreover, we study the problem of stability and stabilization for some classes of singular systems. Finally, we present a numerical example...

Herbivore harvesting and alternative steady states in coral reefs

Ikbal Hossein Sarkar, Joydeb Bhattacharyya, Samares Pal (2021)

Applications of Mathematics

Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability...

Currently displaying 101 – 120 of 358