Global stability and oscillations in classical Lotka-Volterra loops

The paper considers the classical Volterra system of n (⩾ 3) species in predator-prey relation forming a loop, and derives some global properties of its solutions. Sufficient conditions for global asymptotic stability in terms of parameters are obtained, and also the region of global boundedness in the parameter space is indicated. Lastly a three species system is discussed in detail in relation to its global stability, unboundedness of solutions, existence of periodic and non-periodic oscillations.

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