Nonmonotone systems decomposable into monotone systems with negative feedback

Motivated by the work of Angeli and Sontag [1] and Enciso and Sontag [7] in control theory, we show that certain flnite and inflnite dimensional semi-dynamical systems with \negative feedback" can be decomposed into a monotone \open loop" system with \inputs" and a decreasing \output" function. The original system is reconstituted by \plugging the output into the input". Employing a technique of Gouz¶ [9] and Cosner [5] of imbedding the system into a larger symmetric monotone system, we are able to obtain information on the asymptotic behavior of solutions, including existence of positively invariant sets and global convergence.

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