https://doi.org/10.1140/epjs/s11734-024-01356-3
Regular Article
Fractional order sunflower equation: stability, bifurcation and chaos
School of Mathematics and Statistics, University of Hyderabad, 500046, Hyderabad, Telangana, India
Received:
25
April
2024
Accepted:
1
October
2024
Published online:
16
October
2024
The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional order generalization to this delay differential equation. The equation contains two fractional orders and infinitely many equilibrium points. The problem is important because the coefficients in the linearized equation near the equilibrium points are delay dependent. We provide a detailed stability analysis of each equilibrium point using linearized stability. We find the boundary of the stable region by setting the purely imaginary value to the characteristic root. This gives the conditions for the existence of the critical values of the delay at which the stability properties change. We observed the following bifurcation phenomena: stable for all the delay values, a single stable region in the delayed interval, and a stability switch. We also observed a multi-scroll chaotic attractor for some values of the parameters.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjs/s11734-024-01356-3.
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