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.

scholarly journals Exponential Stability of Markovian Jumping Memristor-Based Neural Networks via Event-Triggered Impulsive Control Scheme

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 32564-32574
Author(s):  
Nijing Yang ◽  
Yongbin Yu ◽  
Shouming Zhong ◽  
Xiangxiang Wang ◽  
Kaibo Shi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Impulsive Control ◽  
Markovian Jumping ◽  
Control Scheme ◽  
Event Triggered

scholarly journals Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yanyan Wang ◽  
Jianping Zhou
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Activation Functions ◽  
Discontinuous Activation ◽  
Globally Exponential Stability ◽  
Discontinuous Activation Functions

Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property ofM-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.

scholarly journals Delay-Dependent Exponential Stability for Uncertain Neutral Stochastic Systems with Mixed Delays and Markovian Jumping Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Huabin Chen
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Mixed Delays ◽  
Time Varying ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Globally Exponential Stability ◽  
Neutral Stochastic Systems ◽  
Delay Dependent ◽  
Stability In Mean Square

This paper is mainly concerned with the globally exponential stability in mean square of uncertain neutral stochastic systems with mixed delays and Markovian jumping parameters. The mixed delays are comprised of the discrete interval time-varying delays and the distributed time delays. Taking the stochastic perturbation and Markovian jumping parameters into account, some delay-dependent sufficient conditions for the globally exponential stability in mean square of such systems can be obtained by constructing an appropriate Lyapunov-Krasovskii functional, which are given in the form of linear matrix inequalities (LMIs). The derived criteria are dependent on the upper bound and the lower bound of the time-varying delay and the distributed delay and are therefore less conservative. Two numerical examples are given to illustrate the effectiveness and applicability of our obtained results.

scholarly journals Asymptotic Stability and Exponential Stability of Impulsive Delayed Hopfield Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Chen ◽  
Xiaodi Li ◽  
Dequan Wang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Uniform Asymptotic Stability ◽  
Linear Matrix Inequality Approach

A criterion for the uniform asymptotic stability of the equilibrium point of impulsive delayed Hopfield neural networks is presented by using Lyapunov functions and linear matrix inequality approach. The criterion is a less restrictive version of a recent result. By means of constructing the extended impulsive Halanay inequality, we also analyze the exponential stability of impulsive delayed Hopfield neural networks. Some new sufficient conditions ensuring exponential stability of the equilibrium point of impulsive delayed Hopfield neural networks are obtained. An example showing the effectiveness of the present criterion is given.

scholarly journals Global Asymptotic Stability of Impulsive CNNs with Proportional Delays and Partially Lipschitz Activation Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xueli Song ◽  
Jigen Peng
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Asymptotic Stability ◽  
Cellular Neural Networks ◽  
Variable Coefficients ◽  
Activation Functions ◽  
Proportional Delays ◽  
Nonlinear Measure

This paper researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation vi(t)=ui(et), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis.

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