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On a class of separable quadratic stochastic operators. (English) Zbl 1267.37057

The authors investigate a class of separable quadratic stochastic operators (SQSOs) meant to extend the theory of Volterra quadratic stochastic operators (Volterra QSOs) that arise in the study of interacting animal populations. Each SQSO is observed to depend upon two quadratic matrices \(A\) and \(B\), being shown that if \(A\) is skew-symmetric, then the corresponding SQSO is a linear operator. This shows that the existing QSO theory, based on the use of such skew-symmetric matrices, would not apply for SQSOs. Finally, for a fixed matrix \(A\), several properties of the set of \(B\)s associated with SQSOs are investigated.

MSC:

37H10 Generation, random and stochastic difference and differential equations
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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