Investigation of the Stability of Continuous Dynamic Systems

Integrated pest management (IPM) is a long-term management strategy and has been proved to be more effective in pest control. To well-understand the mechanism and effect of the action of IPM, the geometric theory of the involved semi-continuous dynamic systems is becoming more and more important. In this work, a geometric approach is applied to analyze the stability of the positive order-one periodic solution in semi-continuous dynamic systems. A stability criterion to test the stability of the order-one periodic solution is established. As an application, a stage-structure model involved chemical control is presented to show the efficiency of the proposed method. The sufficient conditions to insure the existence of the periodic solution are provided. In addition, the number and the stability of the periodic solutions are discussed accordingly. The simulations are carried out to verify the results.

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A parametric family of Massey-type methods: inference, prediction, and sensitivity

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2019-0071 ◽

2020 ◽

Vol 16 (3) ◽

pp. 255-269

Author(s):

Enrico Bozzo ◽

Paolo Vidoni ◽

Massimo Franceschet

Keyword(s):

Quantitative Analysis ◽

Control Theory ◽

Dynamic Systems ◽

Parametric Family ◽

Time Varying ◽

Multi Agent ◽

Key Features ◽

The Stability ◽

Agent Coordination ◽

Time Aware

AbstractWe study the stability of a time-aware version of the popular Massey method, previously introduced by Franceschet, M., E. Bozzo, and P. Vidoni. 2017. “The Temporalized Massey’s Method.” Journal of Quantitative Analysis in Sports 13: 37–48, for rating teams in sport competitions. To this end, we embed the temporal Massey method in the theory of time-varying averaging algorithms, which are dynamic systems mainly used in control theory for multi-agent coordination. We also introduce a parametric family of Massey-type methods and show that the original and time-aware Massey versions are, in some sense, particular instances of it. Finally, we discuss the key features of this general family of rating procedures, focusing on inferential and predictive issues and on sensitivity to upsets and modifications of the schedule.

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Periodic Solutions in Rotor Dynamic Systems With Nonlinear Supports: A General Approach

Journal of Vibration and Acoustics ◽

10.1115/1.3269840 ◽

1989 ◽

Vol 111 (2) ◽

pp. 187-193 ◽

Cited By ~ 51

Author(s):

C. Nataraj ◽

H. D. Nelson

Keyword(s):

Dynamic Systems ◽

Original Problem ◽

Squeeze Film ◽

Algebraic Equations ◽

Trigonometric Collocation ◽

Nonlinear Algebraic Equations ◽

The Stability ◽

Future Work ◽

Rotor Dynamic ◽

Large Rotor

A new quantitative method of estimating steady state periodic behavior in nonlinear systems, based on the trigonometric collocation method, is outlined. A procedure is developed to analyze large rotor dynamic systems with nonlinear supports by the use of the above method in conjunction with Component Mode Synthesis. The algorithm discussed is seen to reduce the original problem to solving nonlinear algebraic equations in terms of only the coordinates associated with the nonlinear supports and is a big improvement over commonly used integration methods. The feasibility and advantages of the procedure so developed are illustrated with the help of an example of a typical rotor dynamic system with an uncentered squeeze film damper. Future work on the investigation of the stability of the periodic response so obtained is outlined.

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Successive parameter estimation of continuous dynamic systems

International Journal of Systems Science ◽

10.1080/00207728808547151 ◽

1988 ◽

Vol 19 (7) ◽

pp. 1149-1158 ◽

Cited By ~ 1

Author(s):

CHING-TIEN LIOU ◽

YI-SHYONG CHOU

Keyword(s):

Parameter Estimation ◽

Dynamic Systems ◽

Continuous Dynamic

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An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

Abstract and Applied Analysis ◽

10.1155/2012/956359 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13

Author(s):

Ying Wang ◽

Baodong Zheng ◽

Chunrui Zhang

Keyword(s):

Dynamic Systems ◽

Real Coefficient ◽

Coupled Systems ◽

Decomposition Technique ◽

Exponential Polynomials ◽

Basic Theorem ◽

Algebraic Criterion ◽

The Stability

We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.

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