Nonlinear Dynamics and Applications

AMIGÓ, JOSÉ M.; MONTANI, FERNANDO

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Año: 2025 vol. 27 p. 688 - 693

1099-4300

Nonlinear dynamics is the study of dynamical systems in finite dimensions, whetherin discrete or continuous time, in which the evolution equation (a difference or differentialequation, respectively) is not linear in the state variables. A potential resultof nonlinear dynamics is sensitivity to initial conditions (i.e., small perturbations of theinitial condition can lead to large divergences in the corresponding trajectories in the statespace over time), making such systems unpredictable on a given time scale. Sensitivityto initial conditions, popularized as the butterfly effect, is a hallmark of deterministicchaos. As the well-known example of the logistic parabolas shows, it suffices aquadratic term in the evolution equation for a (in this case, one-dimensional) system toexhibit, for suitably chosen parameters, a mind-wobbling complex behavior. And lowdimensionalchaos is just the entry point to an increasingly weird and fascinating world asthe dimension increases.