Abstract
In biological movements, a special class of random walks, the so-called Lévy walk, has been widely observed. It has been shown that Lévy walks outperform normal random walks in terms of search efficiency because of rare, long, straight movements among short steps, and thus the cause of its prevalence is considered to be a consequence of natural selection. However, recent findings suggest that Lévy walks might also be the result of other mechanisms. This suggests that its origins depend on ecological and physical conditions. Although it is crucial to explore the mechanisms of producing Lévy walks by considering various conditions, the generative mechanisms of Lévy walks based on internal states with nonlinear dynamics are less understood. Here, we develop a generative model composed of simple deterministic nonlinear systems and show that the Lévy walk of an autonomous agent can emerge near the critical point, which is between the synchronous and asynchronous states. Furthermore, we show that Lévy walks have maximized sensitivity to a perturbation and can produce diverse behavior, which might be another advantage of Lévy walks. Our results suggest that the commonly observed Lévy walk can be derived from the critical point hypothesis in which biological systems sitting in a critical point between order and disorder receive benefits. This provides new insights into understandings of how and why Lévy walks are prevalent in biological systems.
