Showing papers in "Bulletin of Mathematical Biology in 1982"

TL;DR: A linear spatially distributed model of a chain of neurons and interneurons was investigated in relation to the generation of propagated alpha rhythmic activity and it was found that such a neuronal chain shows propagation properties for frequencies in the alpha band.

TL;DR: The initial rate of aerosol mixing in the human due to the laryngeal jet is shown to be an important factor affecting the deposition of hygroscopic aerosols and can influence the regional TB distribution of dose when submicron NaCl particles grow rapidly enough to deposit by impaction and sedimentation.

TL;DR: It is shown how the results can be utilized in a closed loop feedback control system and the nature of the optimal controller is established.

TL;DR: Models that minimize a geometric feature such as surface or volume are sensitive to variations in x in a different way from those which minimize flow-related parameters, such as power loss due to friction and shear stress.

TL;DR: An eight-parameter model of human mortality provides an effective means for calculating interpolations and extrapolations of abridged life tables, which are useful making population projections and in computer graphics.

TL;DR: This paper proposes an algorithm based on the different roles of Boolean mappings and on the connection structure to analyze the organization of the network and results are obtained about the dynamics of homogeneous networks.

TL;DR: In this article, the authors compare the conditions for the general error optimality of linear systems developed by Kalman with conditions for feasibility of linear models of neuromuscular and physiological control systems and show that there are no simple relationships between the two sets of conditions.

TL;DR: A model for insulin secretion with a storage and a labile compartment, as well as a provisionary factor, is combined with a signal model in which the signal can be the difference between an excitation and an inhibition, or the difference in concentrations inside and outside some cell components.

TL;DR: A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population and it is concluded that standard phase orbits can be misleading.

TL;DR: In this paper, the qualitative behavior of m species predator-prey systems is studied in a graphical approach and it is shown that tree graphs imply global stability for Volterra models and local stability for general models; furthermore, sufficient conditions for loop graphs imply stability and boundedness of the solutions.

TL;DR: The two categories of automata, namely Arbib in a paper entilled ‘Categories of (M,R)-Systems’ represents both simple ( M, R)-systems with variable genetic structure and those with varying genome as subcategories of the category of Automata, are compared.

TL;DR: There exists a theorem that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed and this allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed.

TL;DR: It is shown that an integral equation formulation can be used to obtain a numerical solution associated with this boundary and initial value problem and an illustrative numerical calculation is able to obtain an accurate solution for both the steady and transient problems.

TL;DR: A model of the geometrical structure of arterial bifurcations is proposed in the context of optimality of the bIfurcation as a fluid conducting system and it is shown that a bifURcation can be optimal both globally and locally.

TL;DR: In this model selection is defined as a solution of the deterministic Eigen equation and the random effect is introduced through the mutation term, but the probability of finding the solution expressing the selection is shown to be smallest.

TL;DR: In this article, the effect of keeping all the parameters constant, except the diffusion coefficients, in a pair of reaction-diffusion equations is studied, and it is shown that the stability of the constant solution and the bifurcation points can be easily established by constructing a simple stability diagram.

TL;DR: In this paper, the cycle structure of a completely random net is characterized using a set of indicator variables such as number of cycles, number of cyclic states and length of cycle.

TL;DR: It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit- cycles of multiple-mode limit-cycle systems.

TL;DR: Although a membrane-only model with given parameters can also account for the observed rates of oxygenation of the red cell, the additional incorporation of differential solubilities of oxygen in the different layers of the RBC yields results that indicate a three layer model to be more plausible.

TL;DR: In this article, it was shown that a multitype branching process can be treated as a dynamical system with control terms, which is of particular relevance in the context of cancer diagnosis.

TL;DR: The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin using an implicit-explicit finite difference form of the equations.

TL;DR: In this paper, a nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor is presented, where the information required is essentially that for solution of linearized forms.

TL;DR: In this paper, the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically, and the equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation.

TL;DR: Exact solutions are obtained and discussed for classes of Lotka-Volterra and Leslie-Gower systems governing the interaction of two species, each species characterised by two time-scales: one representing natural growth and the other, the interdependence of the species.

TL;DR: A discrete time stochastic model formulated for the study of common source epidemics is implemented to study an outbreak of toxoplasmosis in Atlanta, Georgia, in 1977 and conclusions are drawn on the basis of the simulations.

TL;DR: The mathematical analysis considers the situation during electrophysiological experiments, where an odour puff is delivered at an exposed olfactory mucosa, where a situation resembles sniffing of odour samples.

TL;DR: In both finite and semi-infinite habitats, it has been shown that the otherwise stable equilibrium state without dispersal remains so with dispersal also, both under flux and reservoir conditions.

TL;DR: A discrete time stochastic model is formulated for the spread of a disease which is transmitted to an uninfected but susceptible individual through an environmental source and not through contact with infected individuals to provide a method for developing a predicted epidemic curve.

TL;DR: N numerically examined more than one million Large Complex Systems of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations with self-regulation term to have some insight on the stability-complexity relationship.

TL;DR: In this article, a semi-Markov process approach is developed to analyse stochastic compartmental systems using straightforward probabilistic arguments and explicit expressions for several characteristics of the k-compartmental systems with a Poisson process input are derived.