Research on a 3D predator-prey evolutionary system in real estate market
type: Item
instance of: scholarly article
title: Research on a 3D predator-prey evolutionary system in real estate market
zbMATH Open document ID: 1398.91465
DOI: 10.1155/2018/6154940
author: Yujing Yang
author: Wenzhe Tang
published in: Complexity
publication date: 2018-09-26T00:00:00Z
review text: Summary: This paper establishes a model on the upstream and downstream relationship among private enterprises, provincial and local officials, and the central government in the real estate market using the population ecology theory of mutual relations among individual species from the perspective of business ecosystem. A dynamic model is introduced and the complex dynamical behaviors of such a predator-prey model are investigated by means of numerical simulation. The local stability conditions and complex dynamics are investigated, and the existence of chaos is discussed in the sense of Marotto theorem; bifurcation diagrams, Lyapunov exponents, sensitivity analysis for initial values, and time history figure of the system are mapped out and discussed. This shows that there are two routes to complicated dynamics, one of which is the cascade of flip bifurcations resulting in periodic cycles (and chaos), and the other one is Neimark-Sacker bifurcation which produces attractive invariant closed curves. We arrive at conclusions that the phenomenon of chaos is harmful to private enterprises, and unstable behavior is often unfavorable. Thus, linear feedback control is applied to drive the model to a stable state when the system exhibits chaotic behaviors, achieving the goal of eliminating the negative effects to a large extent.
Mathematics Subject Classification ID: 91B74
Mathematics Subject Classification ID: 91A22
Mathematics Subject Classification ID: 34H10
zbMATH DE Number: 6944141
zbMATH Keywords: predator-prey evolutionary model
zbMATH Keywords: real estate market
zbMATH Keywords: population ecology
zbMATH Keywords: numerical simulation
zbMATH Keywords: local stability
zbMATH Keywords: complex dynamics
zbMATH Keywords: flip bifurcation
zbMATH Keywords: Neimark-Sacker bifurcation
zbMATH Keywords: linear feedback control
Wikidata QID: Q115521973
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6154940
OpenAlex ID: W2792960991
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description: scientific article; zbMATH DE number 6944141