Hopf Bifurcation, Trends, Cycles, Square Waves, and Chaos

Bjarne S. Jensen ()
Additional contact information
Bjarne S. Jensen: University of Southern Denmark (SDU)

Chapter Chapter 32 in The Elements and Dynamic Systems of Economic Growth and Trade Models, 2025, pp 1177-1196 from Springer

Abstract: Abstract This chapter considers continuous differential equation growth models with a time delay in the productive operation of installed capital. By a local nonlinear analysis, it is demonstrated that the equilibrium becomes unstable in a Hopf bifurcation for sufficiently large delays. Periodic solutions in the form of limit cycles are created in the bifurcation. In a specific example with a CD production function we show the bifurcation is supercritical such that the limit cycles are stable and exist for delays larger than the critical value. By numerical simulations with a CES production function, we show that the model may exhibit “square wave” solutions and “chaos” (aperiodic oscillations) for our single delay differential equation, if the delay is very large. The model phase portrait integrates the phenomena of economic growth and cycles.

Keywords: Continuous differential equation with Time delays; Local nonlinear analysis; Hopf bifurcation; Limit cycles; Square wave solutions; Chaos; CES technology and Delays with Cycles; Square waves and Chaos (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-52493-6_32

Ordering information: This item can be ordered from
http://www.springer.com/9783031524936

DOI: 10.1007/978-3-031-52493-6_32

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().