Two-dimensional maps can model interactions between populations. Despite their simplicity, these dynamical systems can show some complex situations, as multistability or fractal boundaries between basins that lead to remarkable pictures. Some of them are shown and explained here for three different 2D discrete models.

Ahmed [1], considered study of prey-predator model with predator in disease and harvesting. In this article, a ratio-dependent predator-prey model with disease in the prey population is formulated and analyzed. Assuming that prey populations suffered from epidemics and the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours ...

English noun/verb (N/V) pairs (contract, cement) have undergone complex patterns of change between 3 stress patterns for several centuries. We describe a longitudinal dataset of N/V pair pronunciations, leading to a set of properties to be accounted for by any computational model. We analyze the dynamics of 5 dynamical systems models of linguistic populations, each derived from a model of learn...

Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an underlying potential, V . Typically, V has no lower bound and can exhibit switchbacks wherein V changes form when turning points are encountered by the partic...

This article develops a theoretical framework to link dynamical and population genetic models of persistent viral infection. This linkage is useful because, while the dynamical and population genetic theories have developed independently, the biological processes they describe are completely interrelated. Parameters of the dynamical models are important determinants of evolutionary processes su...

Increasing evidence suggests that neural population responses have their own internal drive, or dynamics, that describe how the neural population evolves through time. An important prediction of neural dynamical models is that previously observed neural activity is informative of noisy yet-to-be-observed activity on single-trials, and may thus have a denoising effect. To investigate this predic...