Studying discrete dynamical systems through differential equations

Dynamical Systems and Differential Equations

In this manuscript we introduce some important concepts concerning dynamical systems theory. We devote special attention to studying differential equations from a dynamical systems viewpoint. The introduced concepts are illustrated by examples.

Difference Equations as Discrete Dynamical Systems

Lia Vas Discrete Dynamical Systems . Difference Equations

If values that we monitor changes during discrete periods (for example, in discrete time intervals), the formula above leads to a difference equation or a dynamical system. In this case, we are dealing with a function that depends on discrete integer values – a sequence. Recall that a sequence of real numbers (indexed by nonnegative integers) can be given by listing its terms (for example, 1, 1...

Ordinary Differential Equations and Dynamical Systems

The Dynamical Systems Approach to Differential Equations

This harmony that human intelligence believes it discovers in nature —does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that whi...