Tipping cycles

Instability in Jacobians is determined by the presence of an eigenvalue lying right half plane. The coefficients characteristic polynomial contain information related to specific matrix elements that play a greater destabilising role. Yet circuits, or cycles, constructed multiplying these together, form only subset all cycles comprising given system. This paper looks at three sign-restricted forms terms sets explore how sign structure affects contribute instability. leads quite rich combinatorial among cycle as set size grows within polynomial.