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Discrete Linear Dynamics in the Plane

In: The Elements and Dynamic Systems of Economic Growth and Trade Models

Author

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  • Bjarne S. Jensen

    (University of Southern Denmark (SDU))

Abstract

This chapter extends the results of linear continuous-time dynamics, Chap. 29 , to observations with their solutions from discrete-time linear dynamical system. The linear governing functions may belong to C 1 $${ }^1$$ -class, but continuity fails with respect to solutions (time path) of discrete-time processes (difference equations). Our solution technique is as in Chap. 29 , based on first finding the stationary ratios of the directrix solutions and next the coordinate solutions. The general coordinate solution and initial value problem of the discrete linear dynamic stems are presented in Propositions 31.1–31.2. The configurations of the phase portrait for the discrete-time linear system are analyzed in detail. The discrete-time solutions are embedded in the continuous-time solution of extended linear systems by Theorem 31.1 to which correspond exact analog discrete system matrices.

Suggested Citation

  • Bjarne S. Jensen, 2025. "Discrete Linear Dynamics in the Plane," Springer Books, in: The Elements and Dynamic Systems of Economic Growth and Trade Models, edition 0, chapter 0, pages 1135-1176, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-52493-6_31
    DOI: 10.1007/978-3-031-52493-6_31
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