scholarly journals Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

2022 ◽  
Vol 105 (1) ◽  
Author(s):  
Andrea Marcello Mambuca ◽  
Chiara Cammarota ◽  
Izaak Neri
Keyword(s):  
Dynamical Systems ◽  
Large Networks ◽  
Predator Prey

Automatic Detection of Saddle-Node–Transcritical Interactions

2019 ◽  
Vol 29 (08) ◽  
pp. 1950104
Author(s):  
Lennaert van Veen ◽  
Marvin Hoti
Keyword(s):  
Dynamical Systems ◽  
Automatic Detection ◽  
Special Structure ◽  
Test Functions ◽  
Test Function ◽  
Predator Prey ◽  
Codimension Two ◽  
Codimension One ◽  
Saddle Node ◽  
Transcritical Bifurcations

Dynamical systems with special structure can exhibit transcritical bifurcations of codimension one. In such systems, the interactions of transcritical bifurcations of codimension two can act as organizing centers. We consider saddle-node–transcritical interactions with either one or two zero eigenvalues and show that, using default test functions, the widely used continuation packages MatCont and AUTO classify these interactions as cusp and Bogdanov–Takens bifurcations, respectively. We propose a new test function that distinguishes these singularities and demonstrate its use in the analysis of a predator–prey-nutrient model strained by a toxicant. The details of the implementation are provided, along with test codes for MatCont.

Psycho-Cognitive Aspects of Dynamic Model-Building in Logo: A Simple Population Evolution and Predator/Prey Program

1988 ◽  
Vol 4 (3) ◽  
pp. 227-252 ◽  
Author(s):  
Bruno Vitale
Keyword(s):  
Dynamical Systems ◽  
Dynamic Model ◽  
Model Building ◽  
Mutual Interaction ◽  
Dynamical Models ◽  
Single Population ◽  
Predator Prey ◽  
Population Evolution ◽  
Programming Skills ◽  
Two Populations

A family of simple models, which can be deployed from the case of the growth of a single population to the mutual interaction of two populations in a predators/prey relation, is programmed in LOGO by using the most elementary programming skills. The deployment is followed step by step, by emphasizing the elements of cognitive novelty and the possible cognitive obstructions, more than the possible programming difficulties. This family of models is used to model a way of introducing, through programming experience, dynamical models of change and a first approach to dynamical systems.

scholarly journals Particularity of “Universal resilience patterns in complex networks”

2016 ◽  
Author(s):  
Jean-Francois Arnoldi ◽  
Bart Haegeman ◽  
Tomas Revilla ◽  
Michel Loreau
Keyword(s):  
Social Networks ◽  
Dynamical Systems ◽  
Complex Networks ◽  
Environmental Changes ◽  
Complex Dynamical Networks ◽  
Economic Systems ◽  
Network Resilience ◽  
Technological Systems ◽  
Predator Prey ◽  
Underlying Mechanisms

In a recent Letter to Nature,Gao, Barzel and Barabási 1 describe an elegant procedure to reduce the dimensionality of complex dynamical networks, which they claim reveals “universal patterns of network resilience”, offering “ways to prevent the collapse of ecological, biological or economic systems, and guiding the design of technological systems resilient to both internal failures and environmental changes”. However, Gao et al restrict their attention to systems for which all interactions between nodes are mutualistic. Since antagonism is ubiquitous in natural and social networks, we clarify why this stringent hypothesis is necessary and what happens when it is relaxed. By analyzing broad classes of competitive and predator-prey networks we provide novel insights into the underlying mechanisms at work in Gao et al’s theory, and novel predictions for dynamical systems that are not purely mutualistic.

A Generalist Predator and the Planar Zero-Hopf Bifurcation

2017 ◽  
Vol 27 (03) ◽  
pp. 1750034 ◽  
Author(s):  
Luis Miguel Valenzuela ◽  
Manuel Falconi ◽  
Gamaliel Blé
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Periodic Orbits ◽  
Linear Approximation ◽  
Equilibrium Points ◽  
Generalist Predator ◽  
Predator Prey ◽  
Predator Prey Models ◽  
Bifurcation Process ◽  
Planar Dynamical Systems

A typical approach for searching periodic orbits of planar dynamical systems is through the Hopf bifurcation. In this work we present a family of predator–prey models with a generalist predator which does not exhibit a Hopf bifurcation, but a planar zero-Hopf bifurcation; that means, in the whole bifurcation process the eigenvalues of the linear approximation around the equilibrium points remain as pure imaginary. Similar models with a nongeneralist predator always possess a Hopf bifurcation.

scholarly journals Stability Analysis of the Periodic Solutions of Some Kinds of Predator-Prey Dynamical Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Neslihan Nesliye Pelen
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Semigroup Theory ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Two Dimensions ◽  
The Other ◽  
Functional Responses ◽  
Predator Prey ◽  
Different Types

Analysis of predator-prey dynamical systems that have the functional response which generalizes the other types of functional responses in two dimensions is mainly studied in this paper. The main problems for this study are to detect the if and only if conditions for attaining the periodic solution of the considered system and to find the condition for global asymptotic stability of this solution for some different types of predator-prey systems that are obtained from that system. To get the desired results, some aspects of semigroup theory for stability analysis and coincidence degree theory are used.

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