Abstract We show that the global stability of quasi-polynomial (QP) and Lotka–Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function.

Paper

Global stability and quadratic Hamiltonian structure in Lotka–Volterra and quasi-polynomial systems

Citations: 10

2004

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Abstract

Abstract We show that the global stability of quasi-polynomial (QP) and Lotka–Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Authors

G. Szederkényi, K. Hangos

Journal

Physics Letters A

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