Geodesic
A Generalized Model of Nonlinear Operators of Volterra Type and Lyapunov Functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 188-196

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In some problems of population genetics we deal with studying asymptotic behavior of the trajectory of nonlinear mappings of a simplex into itself. The present paper is devoted to investigation of homeomorphisms of such mappings and asymptotic behavior. Such a homeomorphism allows us to determine the pre-history of a biological system.
Keywords: nonlinear operators, asymptotical behavior, Lyapunov function. 
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Rasul N. Ganikhodzhaev; Mansoor X. Saburov. A Generalized Model of Nonlinear Operators of Volterra Type and Lyapunov Functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 188-196. http://geodesic.mathdoc.fr/item/JSFU_2008_1_2_a6/