References & Citations
Mathematics > Dynamical Systems
Title: Fractional Order Sunflower Equation: Stability, Bifurcation and Chaos
(Submitted on 26 Apr 2024)
Abstract: 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 coefficients in the linearized equation near the equilibrium points are delay-dependent. We provide a detailed stability analysis of each equilibrium point. 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.
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