Ruling Out Positive Lyapunov Exponents by Using the Jacobian’s Second Additive Compound Matrix

Second additive compound matrices of the system’s Jacobian are used to formulate sufficient conditions to rule out existence of attractors with positive Lyapunov exponents. The criteria are expressed in terms of Lyapunov dissipation inequalities or Linear Matrix Inequalities amenable to analytic verification. The results extend applicability of previous existing conditions formulated to discard periodic and almost periodic oscillations. An example of the technique to rule out chaos in certain parameters region of the Lorenz system is discussed.