scholarly journals Influence of rate of resource flow on dynamics of community of people and artificial beings

2021 ◽  
Vol 16 (4) ◽  
pp. 0
Author(s):  
Vladimir Kotov
Keyword(s):  
Differential Equations ◽  
Human Population ◽  
Well Being ◽  
Reproduction Rate ◽  
System Of Differential Equations ◽  
Equilibrium Solutions ◽  
Resource Flow ◽  
Population Sizes ◽  
Decreasing Functions ◽  
Function Constant

We develop and analyze a population model allowing us to examine a system, where people coexist with artificial beings (robots) and the both consume the same resource entering the system. The robot population consists of friendly and aggressive robots that differ in their attitudes towards people. We propose a system of differential equations, which define a dynamics of the populations of people, friendly robots and aggressive robots, and discuss different scenarios of the system evolution including those that lead to disappearance of the human population. We determine conditions that ensure a more or less prosperous future for humanity. We analyze the behavior of the system for different time dependences of the rate of the resource flow (a constant function, a step-like function, constant functions with undershoots and overshoots, a periodic function, monotonically increasing and decreasing functions). Our analysis shows that the dynamics of the rate of the resource flow defines the changes of the tendencies of the population sizes. Among the obtained solutions, there are solutions that lead to an equilibrium between populations. For people this equilibrium may be regarded as favorable if robots prefer to benefit from communication with people, but not from their extermination. However, equilibrium solutions imply a constant or slowly changes of the rate of the resource flow. Short-term changes of the rate of the resource flow modify the balance between the human population and the robot population. Accumulation of the changes can even lead to disappearance of one of the populations. Qualitative analyzes of the proposed system of differential equations along with computer simulations allow us to conclude that there are some necessary conditions for a well-being of the humans and robots. These conditions are as follows. Firstly, the benefit of the robot from communicating with people has to be higher than the benefit from their extermination. Secondly, to prevent the appearance of the aggressive robots the humanity has to regulate effectively the size of its own population. Thirdly, people have to be able to restrict their needs while maintaining the reproduction rate.

scholarly journals Mathematical model for acquiring immunity to malaria: a PDE approach

BIOMATH ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 2107227
Author(s):  
S Y Tchoumi ◽  
Y T Kouakep ◽  
D J M Fotsa ◽  
F G T Kamba ◽  
J C Kamgang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Spectral Radius ◽  
Human Population ◽  
Reproduction Rate ◽  
Basic Reproduction Rate ◽  
Disease Free

We develop a new model of integro-differential equations coupled with a partial differential equation that focuses on the study of the? naturally acquiring immunity to malaria induced by exposure to infection. We analyze a continuous acquisition of immunity after infected individuals are treated. It exhibits complex and realistic mechanisms precised mathematically in both disease free or endemic context and in several numerical simulations showing the interplay between infection through the bite of mosquitoes. The model confirms the (partial) premunition of the human population in the regions where malaria is endemic. As common in literature, we indicate an equivalence of the basic reproduction rate as the spectral radius of a next generation operator.

Stability analysis of a deterministic model of Zika/Dengue co-circulation

2019 ◽  
Vol 12 (04) ◽  
pp. 1950045 ◽  
Author(s):  
Mike Binder ◽  
Sergei S. Pilyugin
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Human Population ◽  
Deterministic Model ◽  
Sir Model ◽  
System Of Differential Equations ◽  
Dengue Viruses ◽  
Si Model ◽  
The Stability

We consider a deterministic model of Zika and Dengue viruses co-circulating in a human population. We study the system of differential equations modeling the dynamics of the diseases that can either be transmitted directly (host-to-host) or indirectly (host-vector-host). We use an SIR model for hosts and an SI model for vectors in the homogeneous populations. The stability of the model has been analyzed both qualitatively and quantitatively.

scholarly journals Outflowing Envelopes From Stars at Arbitrary Optical Depths a New Approach to the Problem

1998 ◽  
Vol 11 (1) ◽  
pp. 381-381
Author(s):  
A.V. Dorodnitsyn
Keyword(s):  
Differential Equations ◽  
Massive Star ◽  
System Of Differential Equations ◽  
Continuous Transition ◽  
Satisfactory Description ◽  
Sonic Point ◽  
New Approach ◽  
Star Evolution ◽  
Matter Flux ◽  
Massive Star Evolution

We have considered a stationary outflowing envelope accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with partially separated radiation at arbitrary optical depths. The obtained systemof differential equations provides a continuous transition of the solution between optically thin and optically thick regions. We analytically derivedapproximate representation of the solution at the vicinity of the sonic point. Using this representation we numerically integrate the system of equations from the critical point to the infinity. Matching the boundary conditions we obtain solutions describing the problem system of differential equations. The theoretical approach advanced in this work could be useful for self-consistent simulations of massive star evolution with mass loss.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 955
Author(s):  
Alamir Elsayed ◽  
Mohamed El-Beltagy ◽  
Amnah Al-Juhani ◽  
Shorooq Al-Qahtani
Keyword(s):  
Kinetic Model ◽  
Differential Equations ◽  
Test Cases ◽  
System Of Differential Equations ◽  
Reactor Model ◽  
Time System ◽  
New Model ◽  
Reactor Dynamics ◽  
Mean And Variance ◽  
The Mean

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.

The Geometry of d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t), and Euclidean Spaces

2006 ◽  
Vol 49 (2) ◽  
pp. 170-184
Author(s):  
Richard Atkins
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Shortest Paths ◽  
Equivalence Problem ◽  
Second Order ◽  
System Of Differential Equations ◽  
Lagrange Equations ◽  
Invariant Functions ◽  
Underlying Geometry ◽  
The Relationship

AbstractThis paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are defined as the solutions to a pair of second-order differential equations: the Euler–Lagrange equations of the metric. We ask when the converse holds, that is, when solutions to a system of differential equations reveals an underlying geometry. Specifically, when may the solutions to a given pair of second order ordinary differential equations d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t) be reparameterized by t → T(y, t) so as to give locally the geodesics of a Euclidean space? Our approach is based upon Cartan's method of equivalence. In the second part of the paper, the equivalence problem is solved for a generic pair of second order ordinary differential equations of the above form revealing the existence of 24 invariant functions.

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

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