Abstract Competitive Systems and Orbital Stability in R
نویسندگان
چکیده
COMPETITIVE SYSTEMS AND ORBITAL STABILITY IN R RAFAEL ORTEGA AND LUIS ÁNGEL SÁNCHEZ (Communicated by Hal L. Smith) Abstract. Competitive autonomous systems in R3 have the remarkable property of verifying an analogue of the Poincaré-Bendixon theorem for planar equations. This fact allows us to prove the existence of orbitally stable closed orbits for those systems under easily checkable hypothesis. Our aim is to introduce, by changing the ordering in R3, a new class of autonomous systems for which the preceding results directly extend. As a consequence we shall reinterpret some of the results of R. A. Smith in terms of the theory of monotone systems. Competitive autonomous systems in R3 have the remarkable property of verifying an analogue of the Poincaré-Bendixon theorem for planar equations. This fact allows us to prove the existence of orbitally stable closed orbits for those systems under easily checkable hypothesis. Our aim is to introduce, by changing the ordering in R3, a new class of autonomous systems for which the preceding results directly extend. As a consequence we shall reinterpret some of the results of R. A. Smith in terms of the theory of monotone systems.
منابع مشابه
Global stability for the SEIR model in epidemiology.
The SEIR model with nonlinear incidence rates in epidemiology is studied. Global stability of the endemic equilibrium is proved using a general criterion for the orbital stability of periodic orbits associated with higher-dimensional nonlinear autonomous systems as well as the theory of competitive systems of differential equations.
متن کاملOrbital stability of localized structures via Bäcklund transfomations
The Bäcklund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensional dynamical systems. It has recently been used to study the stability of these special solutions. We offer here a dynamical perspective on the Bäcklund Transform, prove an abstract orbital stability theorem, and dem...
متن کاملStability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-bona-mahony Type
This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves.
متن کاملOn the absoluteness of orbital ω-stability
We show that orbital ω-stability is upwards absolute for א0-presented abstract elementary classes satisfying amalgamation and the joint embedding property (each for countable models). We also show that amalgamation does not imply upwards absoluteness of orbital ω-stability by itself. Suppose that k = (K, k) is an abstract elementary class (or AEC; see [1, 8] for a definition), and let (M,a,N) a...
متن کاملQuantum chemistry studies on structures and electronic properties of the Tolazoline drug on nano structure of fullerene
Tolazoline is a non-selective competitive α-adrenergic receptor antagonist. It is a vasodilator that is used to treat spasms of peripheral blood vessels (as in acrocyanosis).Tolazoline is indicated in the treatment of persistent pulmonary hypertension in the newborn (persistent fetal circulation) when systemic arterial oxygenation cannot be maintained by supplemental oxygen and mechanical venti...
متن کامل