An Extension of Two Species Lotka-Volterra Competition Model

Limiting resource is a angular stone of the interactions between species in ecosystems such as competition, prey-predators and food chain systems. In this paper, we propose a planar system as an extension of Lotka-Voterra competition model. This describes? two competitive species for a single resource? which are affected by intra and inter-specific interference. We give its complete analysis for the existence and local stability of all equlibria and some conditions of global stability. The model exhibits a rich set of behaviors with a multiplicity of coexistence equilibria, bi-stability, tri-stability and occurrence of global stability of the exclusion of one species and the coexistence? equilibrium. The asymptotic behavior and the number of coexistence equilibria are shown by a saddle-node bifurcation of the level of resource under conditions on competitive effects relatively to associated growth rate per unit of resource.Moreover, we determine the competition outcome in the situations of Balanced and Unbalanced intra-inter species competition effects. Finally, we illustrate results by numerical simulations.

In Memoriam: A Tribute to Our Colleague and Friend, Asen L. Dontchev

There is no abstract.

IN MEMORY OF PROF. MARIA MLADENOVA

Recollections of the joint activities? and friendship with Prof. Maria Mladenova, DSc

An algorithm for building and integrating dynamic systems based on reaction networks

In the present work we give an overview and implementation of an algorithm for building and integrating dynamic systems from reaction networks. Reaction networks have their roots in chemical reaction network theory, but their nature is general enough that they can be applied in many fields to model complex interactions. Our aim is to provide a simple to use program that allows for quick prototyping of dynamic models based on a system of reactions. After introducing the concept of a reaction and a reaction network in a general way, not necessarily connected to chemistry, we outlay the algorithm for building its associated system of ODEs. Finally, we give a few example usages where we examine a range of growth-decay models in the context of reaction networks.

BIOMATH - 2021 International Conference and School for Young Scientists

This is a brief report on the BIOMATH-2021 International Conference and School for Young Scientists held in Pretoria, South Africa.

Mathematical modeling of bioprocesses with the use of fractional order derivatives

This work brings together two recently discussed topics: mathematical modeling of a bioreactor and working with derivatives of non-integer order. Generally, it turns out that it is reasonable to replace the integer order derivatives in some of the already well known mathematical models describing bioprocesses with fractional order ones. However, the specific structure of such type of derivatives makes the study of the properties of the models a real challenge. This work contains primary results for modeling of a bioreactor with appropriately selected numerical approximations. Different scenarios are taken into consideration: starting from the simplest one - without mortality and then complicating by adding nonzero mortality term. In the classical case the solution of the system of differential equations describing the process has a specific behaviour in terms of monotonicity. Therefore, the focus of the further examinations is to find out whether it is possible to generalize the model into a fractional order one such that the key properties considering monotonicity still hold. The results show that the latter requires certain dependencies between the orders of the derivatives in the mathematical model. The hypothesis is based on two types of experiments which are described in detail. Lotka-Volterra and Monod specific growth rate are used in the mathematical model. The paper contains figures which illustrate the results from different numerical computations performed via Wolfram Mathematica software.

AMiTaNS -- Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences - Retrospection, Present and Future

The Euro-American Consortium for Promotion of the Application of Mathematics in Technical and Natural Sciences was founded in 2008 as a non-governmental non-profit organization in order to foster the scientific activity and informal international exchange. Since then a main tool to realize this intention and idea became an annual conference called AMiTaNS.

In Memoriam: Prof. Roumen P. Maleev, August 17, 1943 – December 12, 2019

Roumen Petrov Maleev was born on August 17, 1943 in the city of Samokov, Bulgaria. He graduated from the Department of Mathematics at Bucurest University in 1967. In 1970 he was appointed as Assistant in the Faculty of Mathematics and Mechanics of Sofia University “St. Kl. Ohridski”, where he became Associate Professor in 1983 and Full Professor in 2006.R. Maleev specialized in Moscow State University in the scholarly year 1971/72 and in Warsaw University in 1982 (February--April). He defended his PhD in Sofia University “St. Kl. Ohridski” in 1975 and his DSci dissertation in 1996 (also in Sofia University “St. Kl Ohridski”). During 1989-1995 he served as Deputy Dean of the Faculty of Mathematics and Informatics of at Sofia University “St. Kl. Ohridski”. He has been Head of the Department of Mathematical Analysis of the Faculty (1998--2000) and member of the Specialized Scientific Council on Mathematics and Mechanics (1995--2004).Maleev delivered lecture courses as Visiting Professor in South Florida University in the summer term of 1991 and in the Athens University in May-June 1997. He also presented numerous lectures at various international conferences worldwide.The scientific interests of Prof. Maleev were in the fields of Geometry of Banach spaces, Functional Spaces and Operators, Variational Analysis, Mathematical Analysis, Education in Mathematics and Informatics, Numerical Analysis.

Mathematical Analysis of Some Reaction Networks Inducing Biological Growth/Decay Functions.

In this work, we study some characteristics of sigmoidal growth/decay functions that are solutions of dynamical systems. In addition, the studied dynamical systems have a realization in terms of reaction networks that are closely related to the Gompertzian and logistic type growth models. Apart from the growing species, the studied reaction networks involve an additional species interpreted as an environmental resource. The reaction network formulation of the proposed models hints for the intrinsic mechanism of the modeled growth process and can be used for analyzing evolutionary measured data when testing various appropriate models, especially when studying growth processes in life sciences. The proposed reaction network realization of Gompertz growth model can be interpreted from the perspective of demographic and socio-economic sciences. The reaction network approach clearly explains the intimate links between the Gompertz model and the Verhulst logistic model. There are shown reversible reactions which complete the already known non-reversible ones. It is also demonstrated that the proposed approach can be applied in oscillating processes and social-science events. The paper is richly illustrated with numerical computations and computer simulations performed by algorithms using the computer algebra system Mathematica.

On a ''Type I Half-logistic Modified Weibull'' Model: Some Extended Models and Applications

The cumulative distribution function (cdf) corresponding to the 'four parameter extended type I half--logistic modified Weibull (TIHLMW) distribution'' is ...