A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka-Volterra type that result translates into a simple condition on the coefficients.
@article{bwmeta1.element.bwnjournal-article-cmv81i2p285bwm, author = {Janusz Mierczy\'nski}, title = {On peaks in carrying simplices}, journal = {Colloquium Mathematicae}, volume = {79}, year = {1999}, pages = {285-292}, zbl = {0936.34036}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv81i2p285bwm} }
Mierczyński, Janusz. On peaks in carrying simplices. Colloquium Mathematicae, Tome 79 (1999) pp. 285-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv81i2p285bwm/
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