Computational Insights into the Unstable Fixed Point of the Fractional Difference Logistic Map
Year: 2024
Type: article
Abstract: Thedivergence from the unstable fixed point of the fractional difference logistic map is investigated in this paper. In contrary to the classical logistic map, the memory horizon of the fractional difference logistic map reaches the initial condition. And though higher order orbits do not exist in the fractional difference logistic map, a trajectory started at the unstable fixed point may continuously remain at the fixed point as the number of iterations tends to infinity. Such an effect is well known for the classical logistic map, but less so in the fractional difference logistic map. It appears that this effect depends on the accuracy of the floating point arithmetic. It is demonstrated that the divergence from the unstable fixed point of the fractional difference logistic map is a completely computational artifact. Using double precision, approximately 32% values of a from the interval 2.7
Source: Mathematics
DOI: 10.3390/math12233635
Institution: Kaunas University of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4404592640