In this paper, we propose a novel approach to automatically identify plant species using dynamics of plant growth and development or spatiotemporal evolution model (STEM). The online kernel adaptive autoregressive-moving-average (KAARMA) algorithm, a discrete-time dynamical system in the kernel reproducing Hilbert space (RKHS), is used to learn plant-development syntactic patterns from feature-vector sequences automatically extracted from 2D plant images, generated by stochastic L-systems. Results show multiclass KAARMA STEM can automatically identify plant species based on growth patterns. Furthermore, finite state machines extracted from trained KAARMA STEM retains competitive performance and are robust to noise. Automatically constructing an L-system or formal grammar to replicate a spatiotemporal structure is an open problem. This is an important first step to not only identify plants but also to generate realistic plant models automatically from observations.