Asymptotic behaviour of a two-dimensional differential system with non-constant delay

2010 ◽  
Vol 283 (6) ◽  
pp. 879-890 ◽  
Author(s):  
Josef Kalas
Keyword(s):  
Asymptotic Behaviour ◽  
Differential System ◽  
Two Dimensional ◽  
Constant Delay

Asymptotic behaviour of real two-dimensional differential system with a finite number of constant delays

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
Josef Rebenda
Keyword(s):  
Finite Number ◽  
Asymptotic Behaviour ◽  
Differential System ◽  
Asymptotic Properties ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System

AbstractIn this article stability and asymptotic properties of a real two-dimensional system

scholarly journals Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Zdeněk Šmarda ◽  
Josef Rebenda
Keyword(s):  
Finite Number ◽  
Asymptotic Behaviour ◽  
Vector Function ◽  
Differential System ◽  
Asymptotic Properties ◽  
Matrix Functions ◽  
Two Dimensional ◽  
Bounded Solutions ◽  
Complex Valued ◽  
Topological Principle

The asymptotic behaviour of a real two-dimensional differential system with unbounded nonconstant delays satisfying is studied under the assumption of instability. Here, , and are supposed to be matrix functions and a vector function. The conditions for the instable properties of solutions and the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a Lyapunov-Krasovskii functional and the suitable Ważewski topological principle. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one constant or nonconstant delay were studied.

Some ARMA models for dependent sequences of poisson counts

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Joint Distribution ◽  
Autoregressive Process ◽  
Two Dimensional ◽  
Arma Models ◽  
Time Reversibility ◽  
Vector Autoregressive ◽  
Arma Processes ◽  
Vector Autoregressive Process

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

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