The simple chaotic model of passive dynamic walking

Recent findings on the dynamical analysis of human locomotion characteristics such as stride length signal have shown that this process is intrinsically a chaotic behavior. The passive walking has been defined as walking down a shallow slope without using any muscular contraction as an active controller. Based on this definition, some knee-less models have been proposed to present the simplest possible models of human gait. To maintain stability, these simple passive models are compelled to show a wide range of different dynamics from order to chaos. Unfortunately, based on simplifications, for many years the cyclic period-one behavior of these models has been considered as the only stable response. This assumption is not in line with the findings about the nature of walking. Thus, this paper proposes a novel model to demonstrate that the knee-less passive dynamic models also have the ability to model the chaotic behavior of human locomotion with some modifications. The presented novel model can show chaotic behavior as a stable and acceptable answer using a chaotic function in heel-strike condition. The represented chaotic model is also able to simulate different types of motor deficits such as Parkinson's disease only by manipulating the value of chaotic parameter. Our model has extensively examined in complexity and chaotic behavior using different analytical methods such as fractal dimension, bifurcation and largest Lyapunov exponent, and it was compared with conventional passive models and the stride signal of healthy subjects and Parkinson patients.