Global Stability, Two Conjectures and Maple
نویسندگان
چکیده
We prove this conjecture in case (a) and signi cantly extend the range of p and q for which it is known in case (b). In cases (a) and (b), these questions are equivalent to global stability of the xed point (L;L) of the planar map (u; v) = (v; f(u; v)). For as in case (a), we consider natural four dimensional extensions T of 3 and S of . For 0 q < p, we prove that (L;L; L; L) is a global stable xed point of T , but we also describe precisely a range of parameters 0 q < p for which S has at least three distinct xed points in the positive orthant. We describe (Section 3) some general principles underlying our arguments. Symbolic calculations using Maple play a crucial role in our arguments in Section 4.
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