Dynamical analysis of a model of social behavior: Criminal vs non-criminal population

Title

Dynamical analysis of a model of social behavior: Criminal vs non-criminal population

Creator

Abbas S.; Tripathi J.P.; Neha A.A.

Description

In this paper, we construct a model motivated by the well known predator-prey model to study the interaction between criminal population and non-criminal population. Our aim is to study various possibilities of interactions between them. First we model it using simple predator-prey model, then we modify it by considering the logistic growth of non-criminal population. We clearly deduce that the model with logistic growth is better than classical one. More precisely, the role of carrying capacity on the dynamics of criminal minded population is discussed. Further, we incorporate law enforcement term in the model and study its effect. The result obtained suggest that by incorporating enforcement law, the criminal population reduces from the very beginning, which resembles with real life situation. Our result indicates that the criminal minded population exist as long as coefficient of enforcement lc does not cross a threshold value and after this value the criminal minded population extinct. In addition, we also discuss the occurrence of saddle-node bifurcation in case of model system with law enforcement. Numerical examples and simulations are presented to illustrate the obtained results. 2017 Elsevier Ltd

Source

Chaos, Solitons and Fractals, Vol-98, pp. 121-129.

Date

2017-01-01

Publisher

Elsevier Ltd

Subject

Criminal-minded population; Logistic growth; Prey predator model; Stability analysis

Coverage

Abbas S., School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175001, H.P., India; Tripathi J.P., Department of Mathematics, Central University of Rajasthan, NH-8, Bandarsindri, Kishangarh, Distt., Ajmer, 305801, Rajasthan, India; Neha A.A., Department of Mathematics, Christ University, Bengaluru, 560029, Karnataka, India

Rights

Restricted Access

Relation

ISSN: 9600779; CODEN: CSFOE

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1016/j.chaos.2017.03.027

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015380962&doi=10.1016%2fj.chaos.2017.03.027&partnerID=40&md5=445380b8dedb83ae670008247aa867fb