Periodic tridiagonal systems modeling competitive-cooperative ecological interactions

Periodic Tridiagonal Systems Modeling Competitive-cooperative Ecological Interactions†

The dynamics of the Poincaré map, associated with a periodic tridiagonal system modeling cooperative-competitive ecological interactions, has been investigated. It is shown that the limit-set is either a fixed point or is contained in the boundary of the positive cone and itself contains a cycle of fixed points. Furthermore, the dynamics is trivial if the number of interactive species is not gr...

A Lyapunov function for tridiagonal competitive-cooperative systems

We construct a Lyapunov function for a tridiagonal competitive-cooperative systems. The same function is a Lyapunov function for Kolmogorov tridiagonal systems, which are defined on a closed positive orthant in Rn. We show that all bounded orbits converge to the set of equilibria. Moreover, we show that there can be no heteroclinic cycles on the boundary of the first orthant, extending the resu...

Dynamics of nonautonomous tridiagonal competitive-cooperative systems of differential equations

Skew-product flow which is generated by a nonautonomous recurrent tridiagonal competitive-cooperative system of differential equations is considered. It is shown that any minimal set is an almost 1-1 extension of the base flow and any ω-limit set contains at most two minimal sets, which generalizes the results of J. Smillie [SIAM J. Math. Anal., 15(1984), pp. 530–534] in autonomous cases and H....

Periodic solutions in modelling lagoon ecological interactions.

In this paper we present and analyze a nutrient-oxygen-phytoplankton-zooplankton mathematical model simulating lagoon ecological interactions. We obtain sufficient conditions, based on principal eigenvalue criteria -- for the existence of periodic solutions. A decoupled model which arises in the high nutrient regime is then considered in further detail for gathering some explicit conditions on ...

On Structuring Cooperative and Competitive Concurrent Systems