The Hyers–Ulam and Ger Type Stabilities of the First Order Linear Differential Equations

2011 ◽  
pp. 191-199
Author(s):  
Takeshi Miura ◽  
Go Hirasawa
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

Control and synchronization of a hyperchaotic finance system via single controller scheme

2015 ◽  
Vol 8 (4) ◽  
pp. 330-344 ◽  
Author(s):  
Ping He ◽  
Yangmin Li
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Content Type ◽  
Order Linear ◽  
Finance System ◽  
First Order ◽  
Single Controller ◽  
Linear Differential ◽  
The Stability ◽  
Control And Synchronization

Purpose – The purpose of this paper is to study the control and synchronization of the hyperchaotic finance system. Design/methodology/approach – A single controller scheme is introduced. The Routh-Hurwitz criteria and the structure of solution of first-order linear differential equations are adopted in analysis of control and synchronization. Findings – Two single controllers are designed and added to the new hyperchaotic finance system. The stability of the hyperchaotic finance system at its zero equilibrium point is guaranteed by applying the appropriate single controller signal based on Routh-Hurwitz criteria. Another effective controller is also designed for the global asymptotic synchronization on the hyperchaotic finance system based on the structure of solution of first-order linear differential equations. Numerical simulations are demonstrated to verify the effectiveness of the proposed single controller scheme. Originality/value – The introduced approach is interesting for control and synchronization the hyperchaotic finance system.

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