Complexity in the muscular blood vessel model with variable fractional derivative and external disturbances

Abstract

In this paper, a variable fractional-order muscular blood vessel system under the influence of different external disturbances is proposed. Specifically, those external disturbances includes periodic forces, stochastic signal and time delay force. Its dynamical analysis is then carried out by employing the bifurcation diagram and phase portraits. Meanwhile, multiscale C0 complexity measure and multiscale 0–1 test are applied to analyze complexity and to detect chaos. It shows that the multiscale coarse graining process deduces better analysis results. Rich dynamics and high complexity are found in the system. Specifically, the noise and non-constant derivative order functions make the system more complex such that the risk of vascular disease is increased. It provides a reference for understanding the vascular disease with complex external disturbances.