| Title |
Continuous adaptive stabilization of the unstable period-1 orbit of the fractional difference logistic map |
| Authors |
Uzdila, Ernestas ; Telksnienė, Inga ; Telksnys, Tadas ; Ragulskis, Minvydas |
| DOI |
10.3390/fractalfract9030151 |
| Full Text |
|
| Is Part of |
Fractal and fractional.. Basel : MDPI. 2025, vol. 9, iss. 3, art. no. 151, p. 1-14.. ISSN 2504-3110 |
| Keywords [eng] |
logistic map ; fractional derivative ; stabilization ; unstable orbit |
| Abstract [eng] |
A continuous adaptive stabilization technique for the unstable period-1 orbit of the fractional difference logistic map is presented in this paper. An impulse-based control technique without short oscillatory transients right after the control impulse is designed for the fractional map with a long memory horizon. However, it appears that the coordinate of the unstable period-1 orbit may drift due to the continuous application of the impulsebased control scheme. An adaptive scheme capable of tracking the drifting coordinate of the unstable period-1 orbit is designed and validated by a number of computational experiments. The proposed control scheme is minimally invasive compared to the continuous feedback control as it preserves the model of the system while requiring only a series of sparse, small, instantaneous control impulses to achieve continuous adaptive stabilization of the unstable period-1 orbit of the fractional difference logistic map. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
