In this paper, we present and study a two competing prey and one predator system where during predation both the teams of prey help each other and the rate of predation on both the teams are different. The prey consumption rate per individual of predator is considered as Beddington–DeAngelis type. Beddington–DeAngelis type functional response describes predator feeding rate depending on both the prey and predator density. Ecological significance of considering this type of functional response depends on how frequently a predator encounters another predator while feeding on the same type of prey, resulting in strong intraspecific competition and thereby reducing the predator feeding rate. Firstly we establish persistence and permanence of the system and examine the role of cooperation coefficient. Different conditions for the coexistence of equilibrium solutions are discussed. Then the local asymptotic stability of various equilibrium points and the existence of Hopf bifurcation at the positive equilibrium are carried out to understand the dynamics of the model system. The Kolmogorov analysis of subsystems suggests for the existence of transcritical bifurcation. Sufficient conditions for the nonexistence of periodic orbits of the considered model system have been presented. The analytical results found in this paper are illustrated with the help of numerical examples.
Nonlinear Dynamics – Springer Journals
Published: Jun 4, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera