LDDS: Python package for computing and visualizing Lagrangian Descriptors for Dynamical Systems

Nonlinear dynamical systems are ubiquitous in natural and engineering sciences, such as fluid mechanics, theoretical chemistry, ship dynamics, rigid body dynamics, atomic physics, solid mechanics, condensed matter physics, mathematical biology, oceanography, meteorology and celestial mechanics (Wiggins, 1994 and references therein). There have been many advances in understanding phenomena across these disciplines using the geometric viewpoint of the solutions and the underlying structures in the phase space; for example (MacKay et al., 1984), (V. Rom-Kedar et al., 1990), (Ozorio de Almeida et al., 1990), (V. Rom-Kedar & Wiggins, 1990), (J. D. Meiss, 1992), (Koon et al., 2000), (Waalkens et al., 2005), (J. D. Meiss, 2015), (Wiggins, 2016), (Zhong et al., 2018), (Zhong & Ross, 2020).

Chief among these phase space structures are the invariant manifolds that form a barrier between dynamically distinct solutions. In most nonlinear systems, the invariant manifolds are computed using numerical techniques that rely on some form of linearization around equilibrium points followed by continuation and globalization. However, these methods become computationally expensive and challenging when applied to the high-dimensional phase space of vector fields defined analytically, from numerical simulations or experimental data.