Periodic Tridiagonal Systems Modeling Competitive-cooperative Ecological Interactions†
نویسندگان
چکیده
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 greater than 4.
منابع مشابه
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....
متن کاملA 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...
متن کاملCooperative and Diminutive Interplay between Halogen, Hydride and Cation-σ Interactions
In the present study, the cooperative and diminutive interplay between halogen, hydride, and cation-σ interactions are studied in HMgH···Li+(Na+)···NCCl, Li+(Na+)···HMgH···ClCN and HMgH···ClCN···Li+(Na+) complexes by means of ab initio calculations. To better understand the cooperative or diminutive effects in the ternar...
متن کاملTitle of Project: Optimal harvesting policies of renewable resources for coupled dynamic systems in a periodically fluc-
Many of the most interesting dynamics in the biological world have to do with interactions between species. Mathematical models which incorporate these interactions are required if we hope to simulate these dynamics. In recent years, coupled dynamic systems (competitive species, cooperative (mutualism) species or prey-predator species) are being widely investigated by many researchers. To my kn...
متن کاملCompetitive and cooperative metabolic interactions in bacterial communities.
Revealing the ecological principles that shape communities is a major challenge of the post-genomic era. To date, a systematic approach for describing inter-species interactions has been lacking. Here we independently predict the competitive and cooperative potential between 6,903 bacterial pairs derived from a collection of 118 species' metabolic models. We chart an intricate association betwe...
متن کامل