No-chaos criteria for certain jerky dynamics

Autonomous third-order scalar differential equations or jerky dynamics give n by (x) triple over dot + A (x) triple over dot + B (x) over circle = g(x) are known to constitute an elementary class of dynamical systems that can exhibit chaotic behavior if the nonlinearity g(x), the entering control par ameters and the initial conditions are appropriately chosen. We investigate conditions on g(x) and the control parameters that are necessary for the a ppearance of chaotic behavior in these equations by deriving several analyt ical criteria that exclude chaotic long-time solutions. (C) 2000 Elsevier S cience B.V. All rights reserved.