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Multi-Dimensional, First-Order, Linear Systems: Characterization

In: Discrete Dynamical Systems

Author

Listed:
  • Oded Galor

    (Brown University)

Abstract

This chapter characterizes the trajectory of a vector of state variables in multi-dimensional, first-order, linear dynamical systems. It examines the trajectories of these systems when the matrix of coefficients has real eigenvalues and the vector of state variables converges or diverges in a monotonic or oscillatory fashion towards or away from a steady-state equilibrium that is characterized by either a saddle point or a stable or unstable (improper) node. In addition, it examines the trajectories of these linear dynamical systems when the matrix of coefficients has complex eigenvalues and the system is therefore characterized by a spiral sink, a spiral source, or a periodic orbit.

Suggested Citation

  • Oded Galor, 2007. "Multi-Dimensional, First-Order, Linear Systems: Characterization," Springer Books, in: Discrete Dynamical Systems, edition 1, chapter 0, pages 59-91, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-36776-5_3
    DOI: 10.1007/3-540-36776-4_3
    as

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