A Theory for Singularity and Stability in Two-dimensional Linear Systems
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https://doi.org/10.5890/JVTSD.2022.03.005Abstract
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] Luo, A.C.J. (2011), Regularity and Complexity in Dynamical Systems, Springer: New York.
[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] Luo, A.C.J. (2020), On dynamics of infinite-equilibrium systems, International Journal of Dynamics and Control, 8, 21-43.
[4] Luo, A.C.J. (2019), Bifurcation and stability in Nonlinear Dynamical Systems, Springer: New York.
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PublishedMarch 2022
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Luo, A. C. J. (2026). A Theory for Singularity and Stability in Two-dimensional Linear Systems. Journal of Vibration Testing and System Dynamics, 6(1), 63-105. https://doi.org/10.5890/JVTSD.2022.03.005