A Mathematical Model to describe the herd behaviour considering group defense

Abstract

A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.

Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model

“…The present investigations show that the spectral collocation method is an effective and suitable scheme for solving the nonlinear LE second-order system of FD equations. In the future, the designed method is an alternate promising solver to be exploited to examine the computational models of fluid dynamics, wire coating model, thin-film flow, squeezing flow systems, Jeffery Hamel type of systems, stretching flow problems, calendaring models, food processing systems, and related research areas [50][51][52][53][54] 2.23 10 −9 × 2.59 10 −9 × 6.10 10 −9 × 8.50 10 −9 × 4.55 10 −9 × 7.78 10 −9 × Figure 7: E convergence of Problem III. Funding: The first author is partially supported by Ministerio de Ciencia, Innovación y Universidades grant number PGC2018-097198-B-I00 and Fundación Séneca de la Región de Murcia grant number 20783/PI/18.…”

A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

“…Statistical interpretation of findings through performance indices of TIC, EVAF, and ENSE based on 60 executions/trials of the solver for obtaining the solution of singular periodic non-linear model validate the trustworthiness, accurateness and robustness. Moreover, the values of the mean, median and semi interquartile range tabulated in Tables 1, 2 provide the precise and accurate values of the presented scheme ANN-PSO-IPS. In future, the designed approach is a promising alternate solver to be exploited/explored to investigate the computational fluid dynamics problems, especially thin film flow, wire coating analysis, squeezing flow models, Jeffery Hamel flow, calendaring problems, stretching flow problems, food processing models, and related fields [57][58][59][60][61][62].…”

Comparative Analysis of Hybrid Fuzzy MCGDM Methodologies for Optimal Robot Selection Process

“…Generalized trapezoidal numbers reduce the computational cost for a transportation problem using GITrFNs, as proposed by Ebrahimnejad [12]. Mathematical modeling and solutions to the models are important and their importance can be seen in management, social, and engineering applications [13][14][15][16][17][18][19][20][21]. Rashid, Beg, and Husnine [22] proposed an extended technique for order preference by similarity to the ideal solution (TOPSIS), which uses GITrFNs for the selection of robots considering both objective and subjective criteria but lacks a weights deriving procedure.…”

“…Weighted normalized ratings were calculated using aggregated weights of criteria from Table 4 and using normalized ratings of robots with respect to criteria in Table 7 and were recorded in Table 8. GITrF-PIS and GITrF-NIS were calculated using Equations (16) and (17) and were recorded in Table 9; here C 1 , C 2 , C 3 and C 5 are benefit criteria and C 4 and C 6 are non-benefit criteria.…”