Digital Computer Simulation of an Ecological System, Based on a Modified Mass Action Law (original) (raw)
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Chaos, Solitons & Fractals, 2002
A fairly realistic three-species food chain model based on the Leslie±Gower scheme is investigated by using tools borrowed from the nonlinear dynamical systems theory. It is observed that two co-existing attractors may be generated by this ecological model. A type-I intermittency is characterized and a homoclinic orbit is found. Ó : S 0 9 6 0 -0 7 7 9 ( 0 0 ) 0 0 2 3 9 -3
Modeling Of Species Interaction in a Habitat Using Lotka- Volterra Type Systems
Mathematical models have been useful in the area of modeling of real life situations; its application can be found in virtually all spheres of scientific researches. As such, we adopt its use in the field of ecology where preys have to compete with other prey for survival. In this paper, we considered Lotka-Volterra type systems, consisting of two first order differential equations which were used to model the population size of prey-predator interaction. We also proposed a system of first order differential equations to model the population sizes of a prey and two predators. Under these conditions one of the predators dies out while the remaining predator and prey approach periodic behavior as time increases. Also we model the population size of two preys and one predator where there may be interaction between the preys. Under these conditions we found that one of the preys died out while the remaining preys and predators approached periodic behavior as time increased. For critical cases, each positive solution of the system was seen to be periodic in nature. Various examples and results were presented and further study was proposed.
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Periodicals of Engineering and Natural Sciences (PEN), 2016
In this paper we extend our previous results in dual approach to analysis and simulation of a complex ecological system of preys and predators. We first define nonlinear dynamic equations Lotka-Volterra Model (LVM) with three preys and three predators and then simulate the equivalent situation with an Agent Based Model (ABM) which models a variety of species attributes and behaviors using NetLogo simulation environment for ABM model. The idea is that the LVM and ABM methods reinforce each other as the predator-prey models become more complex and their dimensionality rises. In particular LVM's parameters, components of community matrix, can be fine tuned using ABM simulations. Dual approach may be able to answer and qualify some of the long standing ecological paradoxes.
Characterization of Multispecies Living Ecosystems
ukpmc.ac.uk
A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the evolving multispecies living ecosystems. Numerical experiments show that a small perturbation or extinction event may affect many other species in the ecosystem in an avalanche manner. Both the avalanches and the extinction arising from these changes follow a power law, reflecting that the multispecies living ecosytems have the characteristics of self-organized criticality.
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In this work, we present analysis of a scaled time-dependent reaction–diffusion system modeling three competitive species dynamics that is of Lotka–Volterra type for coexistence, permanence and stability. The linear analysis is based on the application of qualitative theory of ordinary differential equations and dynamical systems. We consider two notable spatial discretization methods in conjunction with an adaptive time stepping method to verify the biological wave phenomena of the solutions and present the numerical results in one dimensional space. Adequate numerical resulting are provided in one and two dimensions to justify theoretical investigations. In addition, efficiency of the proposed numerical schemes are justified.
This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by as- suming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that give...
Mathematical Model of the Dynamics of three Different Species in Predator-Prey System
2024
In studying the interrelationships of organisms and their environment, there is need to investigate science of coexistence of two or more species. To this end, it is natural to seek a mathematical formulation of this prey-predator problem and to use it to forecast the behavior of populations of various species at different times (Vahidin, et al., 2017; Ma et al., 2017). Nonlinear differential equations are utilized in the study of Lotka-Volterra prey-predator relationships (Canale, 1970). Mathematical models of the interaction between predator and prey populations are generally expressed as systems of nonlinear ordinary differential equations (Bai and Zhang, 2022; Canale, 1970; Xu and Wu, 2013). In animal ecosystems, interspecies interaction is inevitable (Ashine and Gebru, 2017). Interactions between various species occur on a regular basis when they live in comparable habitats. By offering havens, the natural world can offer a certain level of defense to prey populations (Ashine and Gebru, 2017). Such refugia can help in prolonging prey-predator interactions by reducing the chance of extinction due to predation (Ashine and Gebru, 2017).
A model for the relationship between the interaction pattern of ecosystems and their fate
Ecological Modelling, 2005
The growth of isolated species can be described by simple laws but the fate of ecosystems, where several species interact, is difficult to predict. A crucial point seems to be the identification of regularities in the species interaction patterns that determine the fate of ecosystems. We approach this problem by using an ecosystem of three species whose populations are governed by generalized Lotka-Volterra differential equations. In our model, the species undergo both inter-specific and intra-specific interactions. The inter-specific interactions are positive, null or negative and are parameterized by interaction coefficients ε ij which take values: +1, 0 and −1, respectively. In these conditions, 138 different patterns of interactions (up to species re-labeling) are possible. Two extreme cases for the three intra-specific interactions (self-interactions) are considered: ε ii = −1 and ε ii = 0. We also define derived parameters, calculated from the interaction coefficients, which are relevant to determine the survival of species. Comparison of particular patterns shows that the relationship between interaction structure and survival can be subtle and, a priori, unexpected. For instance, we found that adding a negative interaction to a given pattern may be detrimental, indifferent or even beneficial. The same may happen when adding a positive interaction. To make a systematic study of the relationship between structure and fate, first, we perform a "microscopic" study based on the analysis of individual patterns. As a result, we obtained certain general rules or "theorems" concerning the extreme cases of coexistence and extinction of the three species. Second, in order to cover intermediate cases, where precise rules could not be found, we performed "statistical" studies. These provide the probability of survival and coexistence of species as a function of the values of the interaction derived parameters. Among other results, we found that reciprocal cyclic structures, of both positive and negative interactions, and evenly distributed sign balances of input interactions to the species appear to favor survival and coexistence.