Stochastic numerical investigations for nonlinear three-species food chain system

2021 ◽  
Author(s):  
Zulqurnain Sabir
Keyword(s):  
Food Chain ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Interior Point Algorithm ◽  
Top Predator ◽  
Chain System ◽  
Comparison Of The Results ◽  
Global And Local ◽  
Algorithm Scheme

In this work, three-dimensional nonlinear food chain system is numerically treated using the computational heuristic framework of artificial neural networks (ANNs) together with the proficiencies of global and local search approaches based on genetic algorithm (GA) and interior-point algorithm scheme (IPAS), i.e. ANN–GA–IPAS. The three-dimensional food chain system consists of prey populations, specialist predator and top-predator. The formulation of an objective function using the differential system of three-species food chain and its initial conditions is presented and the optimization is performed by using the hybrid computing efficiency of GA–IPAS. The achieved numerical solutions through ANN–GA–IPAS to solve the nonlinear three-species food chain system are compared with the Adams method to validate the exactness of the designed ANN–GA–IPAS. The comparison of the results is presented to authenticate the correctness of the designed ANN–GA–IPAS for solving the nonlinear three-species food chain system. Moreover, statistical representations for 40 independent trials and 30 variables validate the efficacy, constancy and reliability of ANN–GA–IPAS.

scholarly journals Numerical investigations of the nonlinear smoke model using the Gudermannian neural networks

2021 ◽  
Vol 19 (1) ◽  
pp. 351-370
Author(s):  
Zulqurnain Sabir ◽  
◽  
Muhammad Asif Zahoor Raja ◽  
Abeer S. Alnahdi ◽  
Mdi Begum Jeelani ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Fitness Function ◽  
Absolute Error ◽  
Interior Point Algorithm ◽  
Numerical Investigations ◽  
Runge Kutta Method ◽  
Stochastic Framework ◽  
The Stability ◽  
Comparison Of The Results

<abstract> <p>These investigations are to find the numerical solutions of the nonlinear smoke model to exploit a stochastic framework called gudermannian neural works (GNNs) along with the optimization procedures of global/local search terminologies based genetic algorithm (GA) and interior-point algorithm (IPA), i.e., GNNs-GA-IPA. The nonlinear smoke system depends upon four groups, temporary smokers, potential smokers, permanent smokers and smokers. In order to solve the model, the design of fitness function is presented based on the differential system and the initial conditions of the nonlinear smoke system. To check the correctness of the GNNs-GA-IPA, the obtained results are compared with the Runge-Kutta method. The plots of the weight vectors, absolute error and comparison of the results are provided for each group of the nonlinear smoke model. Furthermore, statistical performances are provided using the single and multiple trial to authenticate the stability and reliability of the GNNs-GA-IPA for solving the nonlinear smoke system.</p> </abstract>

A Stochastic Hierarchical Population System: Excitement, Extinction and Transition to Chaos

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Irina Bashkirtseva ◽  
Tatyana Perevalova ◽  
Lev Ryashko
Keyword(s):  
Mathematical Modeling ◽  
Food Chain ◽  
Analytical Method ◽  
Three Dimensional ◽  
Biological Parameters ◽  
Top Predator ◽  
Population System ◽  
Modeling And Analysis ◽  
Transition To Chaos ◽  
Random Fluctuations

A problem of the mathematical modeling and analysis of noise-induced transformations of complex oscillatory regimes in hierarchical population systems is considered. As a key example, we use a three-dimensional food chain dynamical model of the interacting prey, predator, and top predator. We perform a comparative study of the impacts of random fluctuations on three key biological parameters of prey growth, predator mortality, and the top predator growth. A detailed investigation of the stochastic excitement, noise-induced transition from order to chaos, and various scenarios of extinction is carried out. Constructive abilities of the semi-analytical method of confidence domains in the analysis of the noise-induced extinction are demonstrated.

scholarly journals Soft Computing Paradigms to Find the Numerical Solutions of a Nonlinear Influenza Disease Model

2021 ◽  
Vol 11 (18) ◽  
pp. 8549
Author(s):  
Zulqurnain Sabir ◽  
Ag Asri Ag Ibrahim ◽  
Muhammad Asif Zahoor Raja ◽  
Kashif Nisar ◽  
Muhammad Umar ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Local Search ◽  
Objective Function ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Disease Model ◽  
Numerical Results ◽  
Active Set ◽  
System Equations ◽  
Global And Local

The aim of this work is to present the numerical results of the influenza disease nonlinear system using the feed forward artificial neural networks (ANNs) along with the optimization of the combination of global and local search schemes. The genetic algorithm (GA) and active-set method (ASM), i.e., GA-ASM, are implemented as global and local search schemes. The mathematical nonlinear influenza disease system is dependent of four classes, susceptible S(u), infected I(u), recovered R(u) and cross-immune individuals C(u). For the solutions of these classes based on influenza disease system, the design of an objective function is presented using these differential system equations and its corresponding initial conditions. The optimization of this objective function is using the hybrid computing combination of GA-ASM for solving all classes of the influenza disease nonlinear system. The obtained numerical results will be compared by the Adams numerical results to check the authenticity of the designed ANN-GA-ASM. In addition, the designed approach through statistical based operators shows the consistency and stability for solving the influenza disease nonlinear system.

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

2020 ◽  
Vol 13 (02) ◽  
pp. 2050011 ◽  
Author(s):  
Ved Prakash Dubey ◽  
Rajnesh Kumar ◽  
Devendra Kumar
Keyword(s):  
Fractional Order ◽  
Food Chain ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Time Derivative ◽  
Chain Model ◽  
Homotopy Analysis ◽  
Food Chain Model ◽  
Derivatives Of

This research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives. The offered technique is a fantastic blend of homotopy analysis method (HAM) and Laplace transform (LT) operator and has been used fruitfully in the numerical computation of various fractional differential equations (FDEs). This paper involves the fractional derivatives of Caputo style. The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions. It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only — a fact which authenticates the easiness and soundness of the suggested hybrid scheme. The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations. The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

scholarly journals Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Babatunde Idowu ◽  
Kehinde Oyeleke ◽  
Cornelius Ogabi ◽  
Olasunkanmi Olusola
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Dimensional System

Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

scholarly journals A Three-Species Food Chain System with Two Types of Functional Responses

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Younghae Do ◽  
Hunki Baek ◽  
Yongdo Lim ◽  
Dongkyu Lim
Keyword(s):  
Food Chain ◽  
Equilibrium Points ◽  
Ecological Systems ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Top Predator ◽  
Functional Responses ◽  
Chain System ◽  
Dynamical Behaviors ◽  
Theoretical Results

In recent decades, many researchers have investigated the ecological models with three and more species to understand complex dynamical behaviors of ecological systems in nature. However, when they studied the models with three species, they have just considered the functional responses between prey and mid-predator and between mid-predator and top predator as the same type. However, in the paper, in order to describe more realistic ecological world, a three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is considered. It is shown that this system is dissipative. Also, the local and global stability of equilibrium points of the system is established. In addition, conditions for the persistence of the system are found according to the existence of limit cycles. Some numerical examples are given to substantiate our theoretical results. Moreover, we provide numerical evidence of the existence of chaotic phenomena by illustrating bifurcation diagrams of system and by calculating the largest Lyapunov exponent.

A FOOD CHAIN SYSTEM WITH DENSITY-DEPENDENT BIRTH RATE AND IMPULSIVE PERTURBATIONS

2006 ◽  
Vol 09 (03) ◽  
pp. 223-236 ◽  
Author(s):  
SHUWEN ZHANG ◽  
FENYAN WANG ◽  
LANSUN CHEN
Keyword(s):  
Food Chain ◽  
Birth Rate ◽  
Floquet Theory ◽  
Impulsive Differential Equations ◽  
Impulsive Effect ◽  
Top Predator ◽  
Density Dependent ◽  
Chain System ◽  
Predator Eradication ◽  
Fixed Times

We investigate a three-species food chain system with density-dependent birth rate and impulsive effect concerning biological and chemical control strategy — periodic releasing of natural enemies or spraying pesticide at different fixed times. Conditions for the extinction of the prey and top predator are given. By using the Floquet theory of impulsive differential equations and small amplitude perturbation skills, we consider the local stability of the prey and top predator eradication periodic solution. Further, we obtain the conditions of permanence of the system.

scholarly journals Impulsive Perturbations of a Three-Species Food Chain System with the Beddington-DeAngelis Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Younghae Do ◽  
Hunki Baek ◽  
Dongseok Kim
Keyword(s):  
Numerical Simulations ◽  
Functional Response ◽  
Food Chain ◽  
Control Strategy ◽  
Floquet Theory ◽  
Integrated Control ◽  
Comparison Method ◽  
Top Predator ◽  
Chain System ◽  
Theoretical Results

The dynamics of an impulsively controlled three-species food chain system with the Beddington-DeAngelis functional response are investigated using the Floquet theory and a comparison method. In the system, three species are prey, mid-predator, and top-predator. Under an integrated control strategy in sense of biological and chemical controls, the condition for extinction of the prey and the mid-predator is investigated. In addition, the condition for extinction of only the mid-predator is examined. We provide numerical simulations to substantiate the theoretical results.

Electrochemistry of Symmetrical Ion Channel: Three-Dimensional Nernst-Planck-Poisson Model

2015 ◽  
Vol 363 ◽  
pp. 68-78
Author(s):  
Bogusław Bożek ◽  
H. Leszczyński ◽  
Katarzyna Tkacz-Śmiech ◽  
Marek Danielewski
Keyword(s):  
Time Evolution ◽  
Stationary State ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Poisson Model ◽  
Ionic Transport ◽  
Equation System ◽  
Local Concentration

The paper provides a physical description of ionic transport through the rigid symmetrical channel. A three-dimensional mathematical model, in which the ionic transport is treated as the electrodiffusion of ions, is presented. The model bases on the solution of the 3D Nernst-Planck-Poisson system for cylindrical geometry. The total flux includes drift (convection) and diffusion terms. It allows simulating the transport characteristics at the steady-state and time evolution of the system. The numerical solutions of the coupled differential diffusion equation system are obtained by finite element method. Examples are presented in which the flow characteristics at the stationary state and during time evolution are compared. It is shown that the stationary state is achieved after about 2×10 -8 s since the process beginning. Various initial conditions (channel charging and dimensions) are considered as the key parameters controlling the selectivity of the channel. The model allows determining the flow characteristic, calculating the local concentration and potential across the channel. The model can be extended to simulate transport in polymer membranes and nanopores which might be useful in designing biosensors and nanodevices.

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