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This paper proposes a new discretization method for logistic differential equations, for which the popular forward difference model causes chaos and overshoot unless the discrete-time period is chosen to be sufficiently small. While the exact discrete-time model gives exact values at discrete-time instants, it is not really a logistic equation anymore and requires an up-date of a complex gain at each...
This paper presents an exact method of discretizing a logistic differential equation with a constant term (a class of Riccati equation), which are prevalent in a variety of fields, using a common knowledge in digital control theory. The resulting model gives the value that is exact at the discrete-time instants for any discretization period. Two existing methods that can lead to an exact discrete-time...
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