An Algebraic Approach on Globally Exponential Stability of Polynomial Dynamical Systems

2013 ◽  
Author(s):  
Zhikun She ◽  
Huan Liu ◽  
Haoyang Li
Keyword(s):  
Dynamical Systems ◽  
Exponential Stability ◽  
Algebraic Approach ◽  
Polynomial Dynamical Systems ◽  
Globally Exponential Stability

scholarly journals On Some Symmetries of Quadratic Systems

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1300
Author(s):  
Maoan Han ◽  
Tatjana Petek ◽  
Valery G. Romanovski
Keyword(s):  
Dynamical Systems ◽  
Algebraic Approach ◽  
Symmetry Groups ◽  
Planar Case ◽  
Affine Map ◽  
Polynomial Dynamical Systems ◽  
System A ◽  
Polynomial Map ◽  
Real Quadratic ◽  
General Method

We provide a general method for identifying real quadratic polynomial dynamical systems that can be transformed to symmetric ones by a bijective polynomial map of degree one, the so-called affine map. We mainly focus on symmetry groups generated by rotations, in other words, we treat equivariant and reversible equivariant systems. The description is given in terms of affine varieties in the space of parameters of the system. A general algebraic approach to find subfamilies of systems having certain symmetries in polynomial differential families depending on many parameters is proposed and computer algebra computations for the planar case are presented.

Globally exponential stability of nonlinear impulsive switched systems

2015 ◽  
Vol 97 (5-6) ◽  
pp. 803-810 ◽  
Author(s):  
F. Xu ◽  
L. Dong ◽  
D. Wang ◽  
X. Li ◽  
R. Rakkiyappan
Keyword(s):  
Exponential Stability ◽  
Switched Systems ◽  
Globally Exponential Stability ◽  
Impulsive Switched Systems

scholarly journals Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 579 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Interest Rate ◽  
Asymptotic Stability ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Impulsive Control ◽  
Financial System ◽  
Transition Rates ◽  
Markovian Jumping ◽  
Regional Control ◽  
Globally Exponential Stability

The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

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