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Journal of Vibration Testing and System Dynamics 6(1) (2022) 63--105 | DOI:10.5890/JVTSD.2022.03.005

Albert C. J. Luo

Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, IL62026-1805, USA

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Abstract

In this paper, two-dimensional dynamical systems with constant and linear vector fields are presented. Dynamical systems with one-vari- able vector fields are presented and the singular dynamics of two-dimensional linear systems was discussed. Based on the variable-inde- pendent and variable-crossing linear vector fields, the dynamics based on saddle, sink, source and center equilibriums are discussed. Two-dimensional linear dynamical systems with two linear vector fields are discussed, and local dynamics of the saddle and focus equilibriums are presented. The dynamics and stability of two-dimensional linear dynamical systems are presented comprehensively for a better understanding of dynamical behaviors of the two-dimensional linear systems.

References

1. [1]	Luo, A.C.J. (2011), Regularity and Complexity in Dynamical Systems, Springer: New York.

2. [2]	Luo, A.C.J. (2019), On stability and bifurcation of equilibrium in nonlinear systems, Journal of Vibration Testing and System Dynamics, 3(2), 147-232.

3. [3]	Luo, A.C.J. (2020), On dynamics of infinite-equilibrium systems, International Journal of Dynamics and Control, 8, 21-43.

4. [4]	Luo, A.C.J. (2019), Bifurcation and stability in Nonlinear Dynamical Systems, Springer: New York.