A class of time-fractional-order continuous population models for interacting species with stability analysis

2015 ◽  
Vol 26 (6) ◽  
pp. 1495-1504 ◽  
Author(s):  
S. Saha Ray ◽  
S. Sahoo
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Population Models ◽  
Interacting Species ◽  
Continuous Population ◽  
Order Continuous

Stability analysis of switched fractional-order continuous-time systems

2020 ◽  
Vol 102 (4) ◽  
pp. 2467-2478
Author(s):  
Tian Feng ◽  
Lihong Guo ◽  
Baowei Wu ◽  
YangQuan Chen
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Continuous Time ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Order Continuous

New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Rafał Stanisławski
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Continuous Time ◽  
Transfer Functions ◽  
Analytical Stability ◽  
Discretized Systems ◽  
Siso Systems ◽  
Order Continuous

AbstractThis paper tackles important problems in stable discretization of commensurate fractional-order continuous-time LTI SISO systems based on the Grünwald-Letnikov (GL) difference. New, analytical stability/instability conditions are given for the GL-discretized systems governed by fractional-order transfer functions. A stability preservation analysis is also performed for a class of finite GL approximators.

Spectral collocation method for solving continuous population models for single and interacting species by means of exponential Chebyshev approximation

2018 ◽  
Vol 11 (08) ◽  
pp. 1850109 ◽  
Author(s):  
M. A. Ramadan ◽  
M. A. Abd El Salam
Keyword(s):  
Collocation Method ◽  
Chebyshev Approximation ◽  
Accurate Method ◽  
Population Models ◽  
Spectral Collocation Method ◽  
Logistic Growth ◽  
Spectral Collocation ◽  
Interacting Species ◽  
Continuous Population ◽  
Predator Model

In this paper, an efficient and accurate method is presented to solve continuous population models for single and interacting species using spectral collocation method with exponential Chebyshev (EC) functions. The first problem is a logistic growth model in a population, while the second problem is a prey–predator model: Lotka–Volterra system, the third is a simple 2-species Lotka–Volterra competition model, and the final one is a prey–predator model with limit cycle periodic behavior. The high accuracy of this method is verified through some numerical examples. The obtained numerical results are compared with other methods, showing that the proposed method gives higher accuracy.

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