Consider the competition model given by equations, with p=q=1, and assume fracb_1c_2>fraca_1a_2>fracc_1b_2. The competitors coexist. Critical-window conjecture. There is a critical window c_1∈[c_1^,c_1^] for which, when 0<p<1, there are two interior equilibria and, when 0<q<1, there is no interior equilibrium. Furthermore, there is a critical window c_1∈[c_1^,c_1^] for which, when 0<p<1, there is no interior equilibrium and, when 0<q<1, there are two interior equilibria. This conjecture describes how finite-time extinction changes the interior-equilibrium structure of the classical weak-competition coexistence regime. The supplied text gives no evidence of a proof or disproof.

The critical-parameter conjecture for weak competition equilibria

Consider the competition model given by equations, with $p=q=1$ , and assume

\frac{b_{1}}{c_{2}}>\frac{a_{1}}{a_{2}}>\frac{c_{1}}{b_{2}}.

The competitors coexist. Critical-window conjecture. There is a critical window $c_1\in[c_1^{*},c_1^{**}]$ for which, when $0<p<1$ , there are two interior equilibria and, when $0<q<1$ , there is no interior equilibrium. Furthermore, there is a critical window $c_1\in[c_1^{***},c_1^{****}]$ for which, when $0<p<1$ , there is no interior equilibrium and, when $0<q<1$ , there are two interior equilibria.

This conjecture describes how finite-time extinction changes the interior-equilibrium structure of the classical weak-competition coexistence regime. The supplied text gives no evidence of a proof or disproof.

The critical-parameter conjecture for weak competition equilibria

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