Geodesic
A Peculiar Liapunov Functional for Ternary Reaction-Diffusion Dynamical Systems
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 3, pp. 393-407

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A Liapunov functional $W$, depending - together with the temporal derivative $\dot{W}$ along the solutions - on the eigenvalues via the system coefficients, is found. This functional is ``peculiar'' in the sense that $W$ is positive definite and simultaneously $\dot{W}$ is negative definite, if and only if all the eigenvalues have negative real part. An application to a general type of ternary system often encountered in the literature, is furnished. 
@article{BUMI_2011_9_4_3_a5,
     author = {Rionero, Salvatore},
     title = {A {Peculiar} {Liapunov} {Functional} for {Ternary} {Reaction-Diffusion} {Dynamical} {Systems}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {393--407},
     publisher = {mathdoc},
     volume = {Ser. 9, 4},
     number = {3},
     year = {2011},
     zbl = {1234.35133},
     mrnumber = {2906768},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_3_a5/}
}
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Rionero, Salvatore. A Peculiar Liapunov Functional for Ternary Reaction-Diffusion Dynamical Systems. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 3, pp. 393-407. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_3_a5/