Gegenbauer wavelet quasi‐linearization method for solving fractional population growth model in a closed system

2021 ◽  
Author(s):  
Firdous A. Shah ◽  
Mohd Irfan ◽  
Kottakkaran S. Nisar
Keyword(s):  
Population Growth ◽  
Growth Model ◽  
Closed System ◽  
Linearization Method

scholarly journals Legendre Wavelets Method for Solving Fractional Population Growth Model in a Closed System

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
M. H. Heydari ◽  
M. R. Hooshmandasl ◽  
C. Cattani ◽  
Ming Li
Keyword(s):  
Population Growth ◽  
Growth Model ◽  
Closed System ◽  
General Procedure ◽  
Operational Matrix ◽  
Computational Method ◽  
Wavelet Expansion ◽  
Legendre Wavelets ◽  
New Approach ◽  
Block Pulse Functions

A new operational matrix of fractional order integration for Legendre wavelets is derived. Block pulse functions and collocation method are employed to derive a general procedure for forming this matrix. Moreover, a computational method based on wavelet expansion together with this operational matrix is proposed to obtain approximate solution of the fractional population growth model of a species within a closed system. The main characteristic of the new approach is to convert the problem under study to a nonlinear algebraic equation.

Stochastic Dynamical Theta-Logistic Population Growth Model

2014 ◽  
Vol 2014 (3) ◽  
pp. 1-15
Author(s):  
Morteza Khodabin ◽  
◽  
Neda Kiaee ◽  
Keyword(s):  
Population Growth ◽  
Growth Model

scholarly journals The Dynamics of a Spatial Economic Model with Bounded Population Growth

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yue Zhong
Keyword(s):  
Economic Growth ◽  
Population Growth ◽  
Growth Model ◽  
Explicit Solution ◽  
Capital Accumulation ◽  
Initial Distribution ◽  
Time Behavior ◽  
Continuous Space ◽  
Infinite Dimensional ◽  
Economic Growth Model

We investigate a spatial economic growth model with bounded population growth to obtain the asymptotic behavior of detrended capital in a continuous space. The formation of capital accumulation is expressed by a partial differential equation with corresponding boundary conditions. The capital accumulation interacts with the morphology to affect the optimal dynamics of economic growth. After redrafting the spatial growth model in the infinite dimensional Hilbert space, we identify the unique optimal control and value function when the bounded population growth is considered. With nonnegative initial distribution of capital, the explicit solution of the model is obtained. The time behavior of the explicit solution guarantees the convergence issue of the detrended capital level across space and time.

scholarly journals Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Héctor A. Echavarria-Heras ◽  
Cecilia Leal-Ramírez ◽  
Guillermo Gómez ◽  
Elia Montiel-Arzate
Keyword(s):  
Population Growth ◽  
Growth Model ◽  
Continuous Time ◽  
Extreme Values ◽  
Logistic Map ◽  
Phase Region ◽  
Limiting Factors ◽  
Time Dynamics ◽  
The Law ◽  
Global Trajectory

We examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelford. The ensuing paradigm sets natality and mortality rates to express through extreme values of population growth determining factor. Dynamics through time occur over different growth phases. Transition points are interpreted as thresholds of viability, starvation, and intraspecific competition. In this delivery, we focus on the qualitative study of the global trajectory expressed on continuous time and on exploring the feasibility of analytical results against data on populations growing under experimental or natural conditions. All study cases sustained fittings of high reproducibility both at empirical and interpretative slants. Possible phase configurations include regimes with multiple stable equilibria, sigmoidal growth, extinction, or stationarity. Here, we also outline that the associating discrete-time piecewise model composes the logistic map applied over a particular region of the phase configuration. Preliminary exploratory analysis suggests that the logistic map’s chaos onset could surpass once the orbit enters a contiguous phase region.

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