scholarly journals Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-34
Author(s):  
Mingjing Du ◽  
Pengfei Ning ◽  
Yulan Wang
Keyword(s):  
Collocation Method ◽  
Complex Dynamics ◽  
Sinc Function ◽  
New Approach ◽  
Predator Prey ◽  
Prey System ◽  
Simulation Results ◽  
Pattern Formations ◽  
Theoretical Results ◽  
Good Agreement

Although many kinds of numerical methods have been announced for the predator-prey system, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, in this paper, a new interpolation collocation method is proposed for a class of predator-prey systems with complex dynamics characters. Some complex dynamics characters and pattern formations are shown by using this new approach, and the results have a good agreement with theoretical results. Simulation results show the effectiveness of the method.

scholarly journals Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Xinyou Meng ◽  
Qingling Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Complex Dynamics ◽  
Hybrid Control ◽  
Positive Equilibrium ◽  
Stochastic Fluctuation ◽  
Predator Prey ◽  
Prey System ◽  
Singularity Induced Bifurcation ◽  
Distribution Of Roots ◽  
Theoretical Results

A singular delayed biological economic predator-prey system with and without stochastic fluctuation is proposed. The conditions of singularity induced bifurcation are gained, and a state feedback controller is designed to eliminate such bifurcation. Furthermore, saddle-node bifurcation is also showed. Next, the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation, and the hybrid control strategy is used to control the occurrence of Hopf bifurcation. In addition, some explicit formulas determining the spectral densities of the populations and harvest effort are given when the system is considered with stochastic fluctuation. Finally, numerical simulations are illustrated to verify the theoretical results.

Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yong Yao ◽  
Lingling Liu
Keyword(s):  
Complex Dynamics ◽  
Critical Values ◽  
Predator Population ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Constant Rate ◽  
Risk Of Extinction ◽  
Parameter Values ◽  
Theoretical Results

<p style='text-indent:20px;'>In this paper, we study the dynamics of a Leslie-Gower predator-prey system with hunting cooperation among predator population and constant-rate harvesting for prey population. It is shown that there are a weak focus of multiplicity up to three and a cusp of codimension at most two for various parameter values, and the system exhibits two saddle-node bifurcations, a Bogdanov-Takens bifurcation of codimension two and a Hopf bifurcation as the bifurcation parameters vary. The results developed in this article reveal far more complex dynamics compared to the Leslie-Gower system and show how the prey harvesting and the hunting cooperation affect the dynamics of the system. In particular, there exist some critical values of prey harvesting and hunting cooperation such that the predator and prey populations are at risk of extinction if the intensities of harvesting and hunting cooperation are greater than these critical values. Moreover, numerical simulations are presented to illustrate our theoretical results.</p>

scholarly journals The space spectral interpolation collocation method for reaction-diffusion systems

2021 ◽  
pp. 22-22
Author(s):  
Xiao-Li Zhang ◽  
Wei Zhang ◽  
Yu-Lan Wang ◽  
Ting-Ting Ban
Keyword(s):  
Collocation Method ◽  
Complex Dynamics ◽  
Solution Process ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Spectral Interpolation ◽  
Fractal Calculus ◽  
Pattern Formations ◽  
Good Agreement

A space spectral interpolation collocation method is proposed to study nonlinear reaction-diffusion systems with complex dynamics characters. A detailed solution process is elucidated, and some pattern formations are given. The numerical results have a good agreement with theoretical ones. The method can be extended to fractional calculus and fractal calculus.

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate the theoretical results.

Computation of Madalines' Sensitivity to Input and Weight Perturbations

2006 ◽  
Vol 18 (11) ◽  
pp. 2854-2877 ◽  
Author(s):  
Yingfeng Wang ◽  
Xiaoqin Zeng ◽  
Daniel So Yeung ◽  
Zhihang Peng
Keyword(s):  
Probability Theory ◽  
Computer Simulations ◽  
Structural Characteristics ◽  
Analytical Formula ◽  
Single Neurons ◽  
Important Measure ◽  
Simulation Results ◽  
Theoretical Results ◽  
Good Agreement

The sensitivity of a neural network's output to its input and weight perturbations is an important measure for evaluating the network's performance. In this letter, we propose an approach to quantify the sensitivity of Madalines. The sensitivity is defined as the probability of output deviation due to input and weight perturbations with respect to overall input patterns. Based on the structural characteristics of Madalines, a bottomup strategy is followed, along which the sensitivity of single neurons, that is, Adalines, is considered first and then the sensitivity of the entire Madaline network. Bymeans of probability theory, an analytical formula is derived for the calculation of Adalines' sensitivity, and an algorithm is designed for the computation of Madalines' sensitivity. Computer simulations are run to verify the effectiveness of the formula and algorithm. The simulation results are in good agreement with the theoretical results.

Dynamic Modeling and Simulation of Parallel Mechanisms Using the Virtual Spring Approach

2000 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin ◽  
Li Cheng
Keyword(s):  
Closed Loop ◽  
Differential Algebraic Equations ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
New Approach ◽  
Flexible Links ◽  
Simulation Results ◽  
Loop Constraints ◽  
Virtual Springs ◽  
Good Agreement

Abstract A new approach for the dynamic simulation of parallel mechanisms or mechanical systems is presented in this paper. This approach uses virtual springs and dampers to include the closed-loop constraints thereby avoiding the solution of differential-algebraic equations. Examples illustrating the approach are given and include the four-bar mechanism with both rigid and flexible links as well as the 6-dof Gough-Stewart platform. Simulation results are given for the four-bar linkages and the 6-dof manipulator. The results achieve a good agreement with the results obtained from other conventional approaches.

Complex dynamics of a discrete-time predator-prey system with Holling IV functional response

2016 ◽  
Vol 87 ◽  
pp. 158-171 ◽  
Author(s):  
Qianqian Cui ◽  
Qiang Zhang ◽  
Zhipeng Qiu ◽  
Zengyun Hu
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Complex Dynamics ◽  
Predator Prey ◽  
Prey System

scholarly journals A new study for the global asymptotic stability of a general predator-prey model

2021 ◽  
Author(s):  
Manh Tuan Hoang
Keyword(s):  
Asymptotic Stability ◽  
Functional Response ◽  
Mathematical Analysis ◽  
Global Asymptotic Stability ◽  
Lyapunov Stability Theory ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Theoretical Results

In a previous paper [L. M. Ladino, E. I. Sabogal, Jose C. Valverde, General functional response and recruitment in a predator-prey system with capture on both species, Math. Methods Appl. Sci. 38(2015) 2876-2887], a mathematical model for a predator-prey model with general functional response and recruitment including capture on both species was formulated and analyzed. However, the global asymptotic stability (GAS) of this model was only partially resolved. In the present paper, we provide a rigorously mathematical analysis for the complete GAS of the predator-prey model. By using the Lyapunov stability theory in combination with some nonstandard techniques of mathematical analysis for dynamical systems, the GAS of equilibria of the model is determined fully. The obtained results not only provide an important improvement for the population dynamics of the predator-prey model but also can be extended to study its modified versions in the context of fractional-order derivatives. The theoretical results are supported and illustrated by a set of numerical examples.

scholarly journals Predator-prey interactions under fear effect and multiple foraging strategies

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Susmita Halder ◽  
Joydeb Bhattacharyya ◽  
Samares Pal
Keyword(s):  
Complex Dynamics ◽  
Model Simulation ◽  
Prey Population ◽  
Foraging Strategies ◽  
Generalist Predator ◽  
Hopf Bifurcations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Simulation Results

<p style='text-indent:20px;'>We propose and analyze the effects of a generalist predator-driven fear effect on a prey population by considering a modified Leslie-Gower predator-prey model. We assume that the prey population suffers from reduced fecundity due to the fear of predators. We investigate the predator-prey dynamics by incorporating linear, Holling type Ⅱ and Holling type Ⅲ foraging strategies of the generalist predator. As a control strategy, we have considered density-dependent harvesting of the organisms in the system. We show that the systems with linear and Holling type Ⅲ foraging exhibit transcritical bifurcation, whereas the system with Holling type Ⅱ foraging has a much more complex dynamics with transcritical, saddle-node, and Hopf bifurcations. It is observed that the prey population in the system with Holling type Ⅲ foraging of the predator gets severely affected by the predation-driven fear effect in comparison with the same with linear and Holling type Ⅱ foraging rates of the predator. Our model simulation results show that an increase in the harvesting rate of the predator is a viable strategy in recovering the prey population.</p>

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