In this paper, we extend the autonomous n-Dimensional Volterra Mutualistic System to a non- autonomous system. The condition of persistence and extinction is obtained for each population, and the threshold is established for asymptotically autonomous system.
In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish the rule of compound matrices in a Hilbert space, and obtain the expression of solution to a compound operator equation by using the method of operator semigroup. Our brief results generalize the corresponding results in a finite space.
