Mass Balance Equation Versus Logistic Equation in Food Chains

1997 ◽  
Vol 05 (01) ◽  
pp. 77-85 ◽  
Author(s):  
B. W. Kooi ◽  
M. P. Boer ◽  
S. A. L. M. Kooijman
Keyword(s):  
Mass Balance ◽  
Functional Response ◽  
Food Chain ◽  
Dynamic Systems ◽  
Stable Equilibrium ◽  
Food Chains ◽  
Complex Dynamic ◽  
Equation Versus ◽  
Microbial Food Chain ◽  
Parameter Values

The dynamic behavior of tri-trophic food chains consisting of resources, prey, predator and top-predator is dealt with. We compare a formulation whereby the prey growth is logistic, with a mass balance formulation. In the case of the mass balance formulation both the linear and the hyperbolic functional response are discussed. The consequences of the different formulations on the dynamics of a microbial food chain in chemostat situation are described. Bifurcation diagrams for the nonlinear dynamic systems are given. When the prey grows logistically there is no coexistence of the three species for biologically realistic parameter values for a microbial food chain. The same holds for the mass balance equations with a linear functional response for the prey. For a hyperbolic functional response, however, there is a stable equilibrium for the whole food chain in a rather large region of the parameter space. Furthermore, this model shows more complex dynamic behaviors; besides point attractors, limit cycles and chaotic attractors.

scholarly journals MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

2012 ◽  
Vol 09 ◽  
pp. 334-340 ◽  
Author(s):  
MADA SANJAYA WS ◽  
ISMAIL BIN MOHD ◽  
MUSTAFA MAMAT ◽  
ZABIDIN SALLEH
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Food Chain ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Bifurcation Points ◽  
Dynamical Behaviors ◽  
Practical Life ◽  
Parameter Values ◽  
Chain Interaction

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

scholarly journals Variability as normal as apple pie

2021 ◽  
Vol 7 (s2) ◽  
Author(s):  
Marjolijn Verspoor ◽  
Wander Lowie ◽  
Kees de Bot
Keyword(s):  
Dynamic Systems ◽  
Dynamic Systems Theory ◽  
Complex Dynamic ◽  
Controlled Processes ◽  
Complex Dynamic Systems ◽  
L2 Development ◽  
Limited Degree ◽  
Development Phases ◽  
Longitudinal Case Studies ◽  
Over Time

Abstract In recent studies in second language (L2) development, notably within the focus of Complex Dynamic Systems Theory (CDST), non-systematic variation has been extensively studied as intra-individual variation, which we will refer to as variability. This paper argues that variability is functional and is needed for development. With examples of four longitudinal case studies we hope to show that variability over time provides valuable information about the process of development. Phases of increased variability in linguistic constructions are often a sign that the learner is trying out different constructions, and as such variability can be evidence for change, and change can be learning. Also, a limited degree of variability is inherent in automatic or controlled processes. Conversely, the absence of variability is likely to show that no learning is going on or the system is frozen.

Toward a transdisciplinary integration of research purposes and methods for complex dynamic systems theory: beyond the quantitative–qualitative divide

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Phil Hiver ◽  
Ali H. Al-Hoorie ◽  
Diane Larsen-Freeman
Keyword(s):  
Systems Theory ◽  
Dynamic Systems ◽  
Applied Linguistics ◽  
Integrated Approach ◽  
Dynamic Systems Theory ◽  
Complex Dynamic ◽  
Transdisciplinary Approach ◽  
Complex Dynamic Systems ◽  
Human And Social Sciences ◽  
Starting Point

Abstract Complexity theory/dynamic systems theory has challenged conventional approaches to applied linguistics research by encouraging researchers to adopt a pragmatic transdisciplinary approach that is less paradigmatic and more problem-oriented in nature. Its proponents have argued that the starting point in research design should not be the quantitative–qualitative distinction, or even mixed methods, but the distinction between individual versus group-based designs (i.e., idiographic versus nomothetic). Taking insights from transdisciplinary complexity research in other human and social sciences, we propose an integrative transdisciplinary framework that unites these different perspectives (quantitative–qualitative, individual–group based) from the starting point of exploratory–falsificatory aims. We discuss the implications of this transdisciplinary approach to applied linguistics research and illustrate how such an integrated approach might be implemented in the field.

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