Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy

Ruofeng Rao; Shouming Zhong

doi:10.3934/dcdss.2020280

Article Contents

2021, Volume 14, Issue 4: 1375-1393. Doi: 10.3934/dcdss.2020280

This issue Previous Article New synchronization index of non-identical networks Next Article Event-triggered adaptive fault-tolerant control for multi-agent systems with unknown disturbances

Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy

Ruofeng Rao^1, , and
Shouming Zhong^2,

1.
Department of Mathematics, Chengdu Normal University, Chengdu, 611130, China
2.
College of mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China

^* Corresponding author: Ruofeng Rao
^* Corresponding author: Ruofeng Rao

Received: August 2019

Revised: December 2019

Early access: February 2020

Published: April 2021

The work is supported by the Application basic research project of science and Technology Department of Sichuan Province and the Major scientific research projects of Chengdu Normal University in 2019 (CS19ZDZ01)

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Abstract

The stochastic inflow or withdrawal of funds in the international financial market are both positive or negative external inputs to the domestic financial system. So, in this paper, input-to-state stability criterion of delayed feedback chaotic financial system is investigated, and derived by counterevidence method, Lyapunov functional method, variational method and regional control technique, which was involved to equilibrium solution with the positive interest rate. On the other hand, if these inputs are too small to be ignored, impulse control can be applied to stability analysis of the delayed feedback system, in which the delayed impulse allows the pulse effect to lag for a period of time. The obtained stability criteria show that no matter how complex and chaos the financial system is, high-frequency effective macro-control is conducive to the global asymptotical stability of the economic system, including the open economic model with foreign investment fund inputs. Finally, numerical examples illustrate the effectiveness of all the proposed methods.

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Mathematics Subject Classification: Primary: 34H15, 34K25; Secondary: 34K23.

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Table 1. Comparisons of Theorem 3.1 and [23,Theorem 1]

	[23,Theorem 1]	Theorem 3.1
stability type	exponential stability	input-to-state stability
admitting external inputs	No	Yes
Requirements on initial function	No	boundedness restraint

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Table 2. Comparisons of Theorem 4.1, Corollary 2 and [23,Theorem 2]

	[23,Theorem 2]	Corollary 2	Theorem 4.1
stability type	E-S	A-S	A-S
interest rate	$8.93\%$	$8.93\%$	$8.93\%$
delayed feedback model	No	Yes	Yes
time-delays on impulse	No	$\rho_k\equiv0$	$\rho_k\equiv0.05$

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