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Stability analysis of the five-dimensional energy demand-supply system

Kun-Yi Yang, Chun Xia An (2021)

Kybernetika

In this paper, a five-dimensional energy demand-supply system has been considered. On the one hand, we analyze the stability for all of the equilibrium points of the system. For each of equilibrium point, by analyzing the characteristic equation, we show the conditions for the stability or instability using Routh-Hurwitz criterion. Then numerical simulations have been given to illustrate all of cases for the theoretical results. On the other hand, by introducing the phenomenon of time delay, we...

Stability and Boundedness of Solutions of Some Third-order Nonlinear Vector Delay Differential Equation

Larbi Fatmi, Moussadek Remili (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper investigates the stability of the zero solution and uniformly boundedness and uniformly ultimately boundedness of all solutions of a certain vector differential equation of the third order with delay. Using the Lyapunov–Krasovskiĭ functional approach, we obtain a new result on the topic and give an example for the related illustrations.

Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay

Moussadek Remili, Lynda Damerdji Oudjedi (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this article, we shall establish sufficient conditions for the asymptotic stability and boundedness of solutions of a certain third order nonlinear non-autonomous delay differential equation, by using a Lyapunov function as basic tool. In doing so we extend some existing results. Examples are given to illustrate our results.

Stability and gradient dynamical systems.

Jack K. Hale (2004)

Revista Matemática Complutense

The objective in these notes is to present an approach to dynamical systems in infinite dimensions. It does not seem reasonable to make a comparison of all of the orbits of the dynamics of two systems on non locally compact infinite dimensional spaces. Therefore, we choose to compare them on the set of globally defined bounded solutions. Fundamental problems are posed and several important results are stated when this set is compact. We then give results on the dynamical system which will ensure...

Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

Changjin Xu, Maoxin Liao, Xiaofei He (2011)

International Journal of Applied Mathematics and Computer Science

In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations...

Stability and sliding modes for a class of nonlinear time delay systems

Vladimir B. Răsvan (2011)

Mathematica Bohemica

The following time delay system x ˙ = A x ( t ) + 1 r b q i * x ( t - τ i ) - b ϕ ( c * x ( t ) ) is considered, where ϕ : may have discontinuities, in particular at the origin. The solution is defined using the “redefined nonlinearity” concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given.

Stability and stabilizability of a class of uncertain dynamical systems with delays

Mohammed Saadni, Driss Mehdi (2005)

International Journal of Applied Mathematics and Computer Science

This paper deals with a class of uncertain systems with time-varying delays and norm-bounded uncertainty. The stability and stabilizability of this class of systems are considered. Linear Matrix Inequalities (LMI) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established.

Stability and stabilizability of mixed retarded-neutral type systems

Rabah Rabah, Grigory Mikhailovitch Sklyar, Pavel Yurevitch Barkhayev (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We analyze the stability and stabilizability properties of mixed retarded-neutral type systems when the neutral term may be singular. We consider an operator differential equation model of the system in a Hilbert space, and we are interested in the critical case when there is a sequence of eigenvalues with real parts converging to zero. In this case, the system cannot be exponentially stable, and we study conditions under which it will be strongly stable. The behavior of spectra of mixed retarded-neutral...

Stability and stabilizability of mixed retarded-neutral type systems∗

Rabah Rabah, Grigory Mikhailovitch Sklyar, Pavel Yurevitch Barkhayev (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We analyze the stability and stabilizability properties of mixed retarded-neutral type systems when the neutral term may be singular. We consider an operator differential equation model of the system in a Hilbert space, and we are interested in the critical case when there is a sequence of eigenvalues with real parts converging to zero. In this case, the system cannot be exponentially stable, and we study conditions under which it will be strongly...

Stability and stabilizability of mixed retarded-neutral type systems∗

Rabah Rabah, Grigory Mikhailovitch Sklyar, Pavel Yurevitch Barkhayev (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We analyze the stability and stabilizability properties of mixed retarded-neutral type systems when the neutral term may be singular. We consider an operator differential equation model of the system in a Hilbert space, and we are interested in the critical case when there is a sequence of eigenvalues with real parts converging to zero. In this case, the system cannot be exponentially stable, and we study conditions under which it will be strongly...

Stability criteria of linear neutral systems with distributed delays

Guang-Da Hu (2011)

Kybernetika

In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded...

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