STABILITY OF LYAPUNOV EXPONENTS, WEAK INTEGRAL SEPARATION AND NONUNIFORM DICHOTOMY SPECTRUM

Dichotomy Spectrum ◽

Integral Separation ◽

Linear Differential ◽

The Stability ◽

Necessary And Sufficient ◽

Nonuniform Exponential Dichotomy

In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system is proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical one. Furthermore, the existence of full nonuniform exponential dichotomy spectrum under the condition of weak integral separateness is also presented.

Some Structural Properties of Systolic Tree Automata

Fundamenta Informaticae ◽

10.3233/fi-1989-12409 ◽

1989 ◽

Vol 12 (4) ◽

pp. 571-585

Author(s):

E. Fachini ◽

A. Maggiolo Schettini ◽

G. Resta ◽

D. Sangiorgi

Keyword(s):

Structural Properties ◽

Stability Problem ◽

Sufficient Condition ◽

Tree Automata ◽

The Stability ◽

We prove that the classes of languages accepted by systolic automata over t-ary trees (t-STA) are always either equal or incomparable if one varies t. We introduce systolic tree automata with base (T(b)-STA), a subclass of STA with interesting properties of modularity, and we give a necessary and sufficient condition for the equivalence between a T(b)-STA and a t-STA, for a given base b. Finally, we show that the stability problem for T(b)-ST A is decidible.

Necessary and Sufficient Condition for the Stability of Plane Parallel Inviscid Flow

The Physics of Fluids ◽

10.1063/1.1711237 ◽

1964 ◽

Vol 7 (4) ◽

pp. 557 ◽

Cited By ~ 39

Author(s):

Marshall N. Rosenbluth ◽

Albert Simon

Keyword(s):

Inviscid Flow ◽

Sufficient Condition ◽

Plane Parallel ◽

The Stability ◽

A necessary and sufficient condition for Hyers–Ulam stability of first-order periodic linear differential equations

Applied Mathematics Letters ◽

10.1016/j.aml.2019.106040 ◽

2020 ◽

Vol 100 ◽

pp. 106040 ◽

Cited By ~ 2

Author(s):

Ryuma Fukutaka ◽

Masakazu Onitsuka

Keyword(s):

Differential Equations ◽

Linear Differential Equations ◽

Sufficient Condition ◽

Ulam Stability ◽

First Order ◽

Periodic Linear ◽

Linear Differential ◽

The uniform exponential stability of a class of linear differential–difference equations in a Hilbert space

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500020230 ◽

1981 ◽

Vol 89 (3-4) ◽

pp. 201-215 ◽

Author(s):

Richard Datko

Keyword(s):

Hilbert Space ◽

Phase Space ◽

Exponential Stability ◽

Difference Equations ◽

Sufficient Condition ◽

Uniform Exponential Stability ◽

Linear Differential ◽

SynopsisA necessary and sufficient condition is given for the uniform exponential stability of certain autonomous differential–difference equations whose phase space is a Hilbert space. It is shown that this property is preserved when the delays depend homogeneously on a nonnegative parameter.

A Dynamic Duopoly Game with Content Providers’ Bounded Rationality

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420500959 ◽

2020 ◽

Vol 30 (07) ◽

pp. 2050095 ◽

Author(s):

Hamid Garmani ◽

Driss Ait Omar ◽

Mohamed El Amrani ◽

Mohamed Baslam ◽

Mostafa Jourhmane

Keyword(s):

Bounded Rationality ◽

Chaotic Behavior ◽

Sufficient Condition ◽

Pricing Decisions ◽

Dynamical Behaviors ◽

Duopoly Model ◽

The Stability ◽

Necessary And Sufficient ◽

Dynamic Duopoly

This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs’ rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control.

Positive Stabilization of Linear Differential Algebraic Equation System

International Journal of Differential Equations ◽

10.1155/2016/6346780 ◽

2016 ◽

Vol 2016 ◽

pp. 1-3 ◽

Author(s):

Muhafzan

Keyword(s):

Algebraic Equation ◽

State Feedback ◽

Closed Loop ◽

Equation System ◽

Sufficient Condition ◽

Closed Loop System ◽

Differential Algebraic Equation ◽

Linear Differential ◽

We study in this paper the existence of a feedback for linear differential algebraic equation system such that the closed-loop system is positive and stable. A necessary and sufficient condition for such existence has been established. This result can be used to detect the existence of a state feedback law that makes the linear differential algebraic equation system in closed loop positive and stable.

5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500016553 ◽

1976 ◽

Vol 74 ◽

pp. 71-79

Author(s):

R. Datko

Keyword(s):

Asymptotic Stability ◽

Differential Equations ◽

Difference Equations ◽

Sufficient Condition ◽

Uniform Asymptotic Stability ◽

Linear Ordinary Differential Equations ◽

Linear Differential ◽

SynopsisA necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

A Necessary and Sufficient Condition for the Stability of Nonnegative Interval Discrete Systems

10.23919/acc.1990.4790860 ◽

1990 ◽

Author(s):

B. Shafai ◽

K. Perey ◽

D. Cowley ◽

Y. Chehab

Keyword(s):

Discrete Systems ◽

Sufficient Condition ◽

The Stability ◽

A New Algorithm for Testing the Stability of a Polytope: A Geometric Approach for Simplification

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2801188 ◽

1996 ◽

Vol 118 (3) ◽

pp. 611-615 ◽

Cited By ~ 11

Author(s):

Jinsiang Shaw ◽

Suhada Jayasuriya

Keyword(s):

Characteristic Equation ◽

Robust Stability ◽

Geometric Structure ◽

Geometric Approach ◽

Geometric Interpretation ◽

Sufficient Condition ◽

The Stability ◽

Necessary And Sufficient ◽

Edge Theorem

Considered in this paper is the robust stability of a class of systems in which a relevant characteristic equation is a family of polynomials F: f(s, q) = a0(q) + a1(q)s + … + an(q)sn with its coefficients ai(q) depending linearly on q unknown-but-bounded parameters, q = (p1, p2, …, pq)T. It is known that a necessary and sufficient condition for determining the stability of such a family of polynomials is that polynomials at all the exposed edges of the polytope of F in the coefficient space be stable (the edge theorem of Bartlett et al., 1988). The geometric structure of such a family of polynomials is investigated and an approach is given, by which the number of edges of the polytope that need to be checked for stability can be reduced considerably. An example is included to illustrate the benefit of this geometric interpretation.

Stability Analysis ofθ-Methods for Neutral Multidelay Integrodifferential System

Discrete Dynamics in Nature and Society ◽

10.1155/2007/42540 ◽

2007 ◽

Vol 2007 ◽

pp. 1-8

Author(s):

Y. Xu ◽

J. J. Zhao ◽

Z. N. Sui

Keyword(s):

Numerical Stability ◽

Numerical Experiments ◽

Analytic Solutions ◽

Sufficient Condition ◽

Neutral Delay ◽

Integrodifferential System ◽

System A ◽

The Stability ◽

This paper studies the stability of a class of neutral delay integrodifferential system. A necessary and sufficient condition of stability for its analytic solutions is considered. The improvedθ-methods are developed. Some numerical stability properties are obtained and numerical experiments are given.