Abstract
Riccati or quadratic differential equations are constructed in terms of algebras. The idea is to use the structure of algebras as semisimplicity, radical, automorphisms to help determine the behavior of solutions, decoupling, equilibrium, stability before doing detailed calculations. Examples concerning geodesics, mechanics, predator-prey model, and the general solution are given by algebras. Relationships are given concerning the radical of an algebra and bifurcations, the stability of equilibrium and root space decompositions, the domains of attraction and automorphism groups.
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