Scalar Delay Logistic Equation

This Demonstration shows the solution of a simple scalar logistic delay equation that has found application in chemical engineering problems:
where is the time delay and and are positive constants. The values of the parameters generating bifurcations can be determined analytically [1]. Assuming the parameter values , , chaos occurs for approximately; for large values of all oscillations disappear. Also interesting is the effect of time delay on the generation of chaos: when and , all oscillations disappear at low values of . A necessary and sufficient condition for generating oscillations is , where the frequency is determined from the relationship .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


[1] M. Berezowski, "Effect of Delay Time on the Generation of Chaos in Continuous Systems. One-Dimensional Model. Two-Dimensional Model—Tubular Chemical Reactor with Recycle," Chaos, Solitons and Fractals, 12(1), 2001 pp. 83–89. doi:10.1016/S0960-0779(99)00171-X.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.