Z. Eskandari , J. Alidousti , Z. Avazzadeh , J.A. Tenreiro Machado
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Dynamics and bifurcations of a discrete-time prey-predator model with Allee effect on the prey population
This paper studies the dynamic behavior of a discrete-time prey-predator model. It is shown that this model undergoes codimension one and codimension two bifurcations such as transcritical, flip (period-doubling), Neimark-Sacker and strong resonances 1:2, 1:3 and 1:4. The bifurcation analysis is based on the numerical normal form method and the bifurcation scenario around the bifurcation point is determined by their critical normal form coefficients. The advantage of this method is that there is no need to calculate the center manifold and to convert the linear part of the map to a Jordan form. The bifurcation curves of fixed points under variation of one and two parameters are obtained, and the codimensions one and the two bifurcations on the corresponding curves are computed.
期刊介绍：
Ecological Complexity is an international journal devoted to the publication of high quality, peer-reviewed articles on all aspects of biocomplexity in the environment, theoretical ecology, and special issues on topics of current interest. The scope of the journal is wide and interdisciplinary with an integrated and quantitative approach. The journal particularly encourages submission of papers that integrate natural and social processes at appropriately broad spatio-temporal scales.
Ecological Complexity will publish research into the following areas:
• All aspects of biocomplexity in the environment and theoretical ecology
• Ecosystems and biospheres as complex adaptive systems
• Self-organization of spatially extended ecosystems
• Emergent properties and structures of complex ecosystems
• Ecological pattern formation in space and time
• The role of biophysical constraints and evolutionary attractors on species assemblages
• Ecological scaling (scale invariance, scale covariance and across scale dynamics), allometry, and hierarchy theory
• Ecological topology and networks
• Studies towards an ecology of complex systems
• Complex systems approaches for the study of dynamic human-environment interactions
• Using knowledge of nonlinear phenomena to better guide policy development for adaptation strategies and mitigation to environmental change
• New tools and methods for studying ecological complexity
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