On Discrete-Time Integration Gains and Monotonic Response of Logistic Systems

Y. Habiro and N. Hori (Japan)


Differential logistic equation, discretization, discrete-time integrator gain.


This paper examines existing and new discrete-time models for a continuous-time system governed by a logistic differential equation that has a stable and an unstable equilibrium points. Existing discretization models for the logistic equation are classified in terms of the discrete-time integration gain expressed in delta form. A condition on these models is studied such that their response is monotonic, which results in non-overshooting response and, thus, no chaos. It is shown that models with the gain that is hyperbolic in the state can be non overshooting for any discretization period. It is also shown that monotonic discrete-time models with a gain that is non-hyperbolic can be created. Simulation results are presented to compare performances of these discrete time models.

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