DISCRETE TIME PREY-PREDATOR MODEL WITH GENERALIZED HOLLING TYPE INTERACTION

ABSTRACT We have introduced a discrete time prey-predator model with Generalized Holling type interaction. Stability nature of the fixed points of the model are determined analytically. Phase diagrams are drawn after solving the system numerically. Bifurcation analysis is done with respect to various parameters of the system. It is shown that for modeling of non-chaotic prey predator ecological systems with Generalized Holling type interaction may be more useful for better prediction and analysis

An externally-corrected size-extensive single-root MRCC formalism: its kinship with the rigorously size-extensive state-specific MRCC theory

The rigorously size-extensive intruder-free state-specific multi-reference coupled cluster theory (SSMRCC) developed by Mukherjee and coworkers [J. Chem. Phys. 110 (1999) 6171] makes use of the Jeziorski-Monkhorst Ansatz [Ω = ∑μexp(Tμ)| ΦμΧΦμ|] involving a different cluster operator exp(Tμ) acting on its corresponding model function Φμ. The resulting equations involve a coupling between the cluster operators for all the μ as demanded by the rigorous requirement of size-extensivity. If one wishes a size-extensive formalism where such couplings are minimal, one will have to replace the exact coupling term by hand where only Tμ for a given Φμ appears. In this paper, we propose such an externally corrected size-extensive single-root multi-reference CC (ecsr-MRCC) formalism, which is intruder-free and simpler in structure as compared to the parent SSMRCC theory. Our intention in this paper is not to replace or underplay the efficacy of the rigorous SSMRCC theory, but to indicate how a simple external correction leads to results of similar quality where the coupling of Tμs for various μ are avoided. Kinship of the ecsr-MRCC formalism with the parent SSMRCC, and certain other allied MRCC theories will also be discussed. The performance of the method will be assessed by applying it to H4, BeH2, F2 and CH2, and comparing them against the SSMRCC results, benchmark full CI results (when available), and those from the allied MRCC formalisms. The encouraging results indicate that this simple modification leads to equations with the minimal coupling without unduly sacrificing the accuracy