An algorithm to verify asymptotic stability conditions of a certain family of systems of differential equations

In this particular paper we firstly deal with Samuelson’s model of national economy. We create a difference equation which reflects Samuelson’s model for the national income of a country taking into consideration the expenditure and the investments of the two previous years and not only the immediately previous one. Later we find the saddle-point and deal with its stability giving conditions concerning the coefficient of the difference equation and which are able (sufficient) and necessary in order for the saddle-point to be stable.

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New exponential stability conditions for linear delayed systems of differential equations

10.14232/ejqtde.2016.8.5 ◽

2016 ◽

Cited By ~ 1

Author(s):

Leonid Berezansky ◽

Josef Diblik ◽

Zdenek Svoboda ◽

Zdenek Smarda

Keyword(s):

Differential Equations ◽

Exponential Stability ◽

Stability Conditions ◽

Delayed Systems ◽

Systems Of Differential Equations

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Stability investigation of quadratic systems with delay

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953300000095 ◽

2000 ◽

Vol 13 (1) ◽

pp. 85-92 ◽

Cited By ~ 2

Author(s):

Vladimir Davydov ◽

Denis Khusainov

Keyword(s):

Asymptotic Stability ◽

Quadratic Form ◽

Stability Region ◽

Zero Solution ◽

Stability Conditions ◽

Quadratic Systems ◽

Systems Of Differential Equations ◽

Asymptotic Stability Region ◽

Lyapunov’S Second Method ◽

Form Stability

Systems of differential equations with quadratic right-hand sides with delay are considered in the paper. Compact matrix notation form is proposed for the systems of such type. Stability investigations are performed by Lyapunov's second method with functions of quadratic form. Stability conditions of quadratic systems with delay, uniformly by argument deviation, and with delay depending on the system's parameters are derived. A guaranteed radius of the ball of asymptotic stability region for zero solution is obtained.

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On the subject of influence of dissipative and constant of moments on the stability of uniform rotations of non-free two elastically connected gyroscopes of Lagrange

Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine ◽

10.37069/1683-4720-2020-34-6 ◽

2021 ◽

Vol 34 ◽

pp. 50-61

Author(s):

Yurii Kononov ◽

Yaroslav Sviatenko

Keyword(s):

Fixed Point ◽

Asymptotic Stability ◽

Stability Conditions ◽

Inertial Coordinate System ◽

Resisting Medium ◽

Angular Velocities ◽

The Subject ◽

The Stability ◽

Spherical Hinge ◽

Asymptotic Stability Conditions

The conditions for asymptotic stability of uniform rotations in a resisting medium of two heavy Lagrange gyroscopes connected by an elastic spherical hinge are obtained in the form of a system of three inequalities. The bottom gyroscope has a fixed point. The rotation of the gyroscopes is maintained by constant moments in the inertial coordinate system. The influence of the elasticity of the hinge on the stability conditions is estimated. It is shown that for a sufficiently high rigidity of the hinge, the asymptotic stability conditions are determined by only one inequality, which coincides with the inequality obtained for the case of a cylindrical hinge. When the angular velocities of the gyroscopes' own rotations coincide, this inequality coincides with the well--known condition for one gyroscope. Cases of degeneration of an elastic spherical hinge into a spherical inelastic, cylindrical and universal elastic hinge (Hooke's hinge) are considered. For the Hooke hinge, it is shown that there is no asymptotic stability at a sufficiently high angular velocity of gyroscopes rotation.

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