Mathematical model of three competing populations and multistability of periodic regimes

Purpose of this work is to analyze oscillatory regimes in a system nonlinear differential equations describing the competition three non-antagonistic species spatially homogeneous domain. Methods. Using theory cosymmetry, we establish connection between destruction two-parameter family equilibria and emergence continuous periodic regimes. With help computational experiment MATLAB, search for limit cycles an analysis multistability were carried out. Results. We studied dynamic scenarios competing different coefficients growth interaction. For several combinations parameters experiment, new families (extreme multistability) are found. bistability: coexistence isolated cycles, as well stationary solution regime. Conclusion. found two locating regarding plane passing through corresponding existence only one species. Besides lying plane, possible with intersecting at points. can consider case example processes leading overpopulation subsequent decline numbers. These results will further serve basis systems populations heterogeneous areas.