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Monotone bifurcation graphs

Abstract In recent work by Angeli and the authors, it was shown that the stability and global behaviour of strongly monotone dynamical systems may be profitably studied using a technique that involves feedback decompositions into ‘well-behaved’ subsystems. The present paper generalizes the approach, so that it applies to a far larger class of systems. As an illustration, the techniques are used in the analysis of a nine-variable autoregulatory transcription network. Also, extensions to delay and reaction diffusion systems are considered.