TY - JOUR

T1 - P Matrix Properties, Injectivity, and Stability in Chemical Reaction Systems

AU - Banaji, Murad

AU - Donnell, Pete

AU - Baigent, Stephen

PY - 2007/12/31

Y1 - 2007/12/31

N2 - In this paper we examine matrices which arise naturally as Jacobians in chemical dynamics. We are particularly interested in when these Jacobians are P matrices (up to a sign change), ensuring certain bounds on their eigenvalues, precluding certain behavior such as multiple equilibria, and sometimes implying stability. We first explore reaction systems and derive results which provide a deep connection between system structure and the P matrix property. We then examine a class of systems consisting of reactions coupled to an external rate-dependent negative feedback process and characterize conditions which ensure that the P matrix property survives the negative feedback. The techniques presented are applied to examples published in the mathematical and biological literature.

AB - In this paper we examine matrices which arise naturally as Jacobians in chemical dynamics. We are particularly interested in when these Jacobians are P matrices (up to a sign change), ensuring certain bounds on their eigenvalues, precluding certain behavior such as multiple equilibria, and sometimes implying stability. We first explore reaction systems and derive results which provide a deep connection between system structure and the P matrix property. We then examine a class of systems consisting of reactions coupled to an external rate-dependent negative feedback process and characterize conditions which ensure that the P matrix property survives the negative feedback. The techniques presented are applied to examples published in the mathematical and biological literature.

U2 - 10.1137/060673412

DO - 10.1137/060673412

M3 - Journal article

VL - 67

SP - 1523

EP - 1547

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 6

ER -