Dataset of phase portraits of the fractional prey-predator model with Holling type-II interaction (without predator harvesting)

Description

The need for a fractional generalization of a given classical model is often due to new behaviors which cannot be taken into account by the model. In this situation, it can be useful to look for a fractional deformation of the initial system, trying to fit the fractional exponent of differentiation in order to catch properly the data.

Once we have constructed a viable fractional system satisfying the basic properties, the basic problem is to study its dynamical behavior. However, it is usually not possible to solve the fractional differential equations and to provide explicit solutions. As a consequence, we are leaded to a numerical study of these equations. In general, simulations are used to validate a given continuous model . When this model satisfies fundamental properties like positivity, stability, etc, then one must be sure that the numerical scheme preserves these properties.

We adapt the strategy of R. Mickens to the fractional case in the context of the positivity property. We define a non-standard finite difference scheme for our class of fractional differential systems which preserves positivity.

Mathematical details of fractional generalization and complete analysis of constructed numerical scheme can be found in the paper: “Discrete and continuous fractional persistence problems – the positivity property and applications”, Jacky Cresson, Anna Szafrańska, Commun. Nonlinear Sci. Numer. Simulat. 44 (2017), 424–448.

Presented dataset consists with several phase portraits of the numerical solutions to the fractional prey-predator model with Holling type-II interaction (without predator harvesting). Numerical results are presented with respect to different values of model parameters: a – per capita consumption rate of predator, b - intrinsic growth rate of prey population, c – death rate of predator individuals.

For each set of model parameters ones can find phase portraits for different values of fractional order a = 0.5,0.6,0.7,0.8,0.9,1, with respect of numerical parameters: T – time interval, h – time step, x – initial value for preys, y – initial value for predators.

Dataset file

PhasePortaits.zip

5.9 MB, S3 ETag 0fa3a9e85312a861b8d3099ef5d95e97-1, downloads: 82

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Attribution

Details

Year of publication:

2021

Verification date:

2021-06-07

Dataset language:

English

Fields of science:

mathematics (Natural sciences)

DOI:

10.34808/v4j8-mc42

Verified by:

Gdańsk University of Technology

Keywords

References

publication Discrete and continuous fractional persistence problems – the positivity property and applications

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