Sprott Systems

The Sprott systems are 19 autonomous quadratic systems of three ordinary differential equations exhibiting numerically observed chaos. Sprott (1994) found the systems in a search for simple chaotic flows, labeling them A through S according to their vector fields. Cases A through E have five nonzero terms, of which two are nonlinear, and cases F through S have six nonzero terms, of which one is nonlinear. The variables , , and depend on time, and primes denote derivatives with respect to . For example, case B is

			(1)
			(2)
			(3)

and case F is

			(4)
			(5)
			(6)

The two cases have different equilibria. Case B has and , and case F has and . Their vector fields have constant negative divergence, and , respectively, so both flows contract volume in phase space. In parameterized versions, case B replaces , , and the constant 1 in by , , and , respectively. Case F replaces by .