An analysis of dynamics of discrete demand-inventory model with bifurcation diagrams and phase portraits

2017 ◽  
Author(s):  
Piotr Hachuła ◽  
Magdalena Nockowska-Rosiak ◽  
Ewa Schmeidel
Keyword(s):  
Inventory Model ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Analysis Of Dynamics

scholarly journals Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Piotr Hachuła ◽  
Magdalena Nockowska-Rosiak ◽  
Ewa Schmeidel
Keyword(s):  
Equilibrium Points ◽  
Three Dimensional ◽  
Inventory Model ◽  
Phase Portraits ◽  
Dimensional System ◽  
Planar System ◽  
Stock Level ◽  
Lyapunov Coefficient ◽  
Analysis Of Dynamics ◽  
Dependent Demand

An analysis of dynamics of demand-inventory model with stock-level-dependent demand formulated as a three-dimensional system of difference equations with four parameters is considered. By reducing the model to the planar system with five parameters, an analysis of one-parameter bifurcation of equilibrium points is presented. By the analytical method, we prove that nondegeneracy conditions for the existence of Neimark-Sacker bifurcation for the planar system are fulfilled. To check the sign of the first Lyapunov coefficient of Neimark-Sacker bifurcation, we use numerical simulations. We give phase portraits of the planar system to confirm the previous analytical results and show new interesting complex dynamical behaviours emerging in it. Finally, the economical interpretation of the system is given.

scholarly journals Chaos and Control in Coronary Artery System

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yanxiang Shi
Keyword(s):  
Coronary Artery ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Road ◽  
Two Systems ◽  
And Control

Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

scholarly journals Fear effect in discrete prey-predator model incorporating square root functional response

2021 ◽  
Vol 2 (2) ◽  
pp. 51-57
Author(s):  
P.K. Santra
Keyword(s):  
Functional Response ◽  
Stability Condition ◽  
Discrete Model ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Square Root ◽  
Bifurcation Diagrams ◽  
Fear Effect ◽  
Hypothetical Data ◽  
Predator Model

In this work, an interaction between prey and its predator involving the effect of fear in presence of the predator and the square root functional response is investigated. Fixed points and their stability condition are calculated. The conditions for the occurrence of some phenomena namely Neimark-Sacker, Flip, and Fold bifurcations are given. Base on some hypothetical data, the numerical simulations consist of phase portraits and bifurcation diagrams are demonstrated to picturise the dynamical behavior. It is also shown numerically that rich dynamics are obtained by the discrete model as the effect of fear.

Bifurcation Diagrams and Quotient Topological Spaces Under the Action of the Affine Group of a Family of Planar Quadratic Vector Fields

2015 ◽  
Vol 25 (11) ◽  
pp. 1550150 ◽  
Author(s):  
Oxana Cerba Diaconescu ◽  
Dana Schlomiuk ◽  
Nicolae Vulpe
Keyword(s):  
Parameter Space ◽  
Group Action ◽  
Sufficient Conditions ◽  
Phase Portraits ◽  
Topological Spaces ◽  
Canonical Forms ◽  
Affine Transformations ◽  
Bifurcation Diagrams ◽  
Dimensional Parameter ◽  
Quotient Spaces

In this article, we consider the class [Formula: see text] of all real quadratic differential systems [Formula: see text], [Formula: see text] with gcd (p, q) = 1, having invariant lines of total multiplicity four and two complex and one real infinite singularities. We first construct compactified canonical forms for the class [Formula: see text] so as to include limit points in the 12-dimensional parameter space of this class. We next construct the bifurcation diagrams for these compactified canonical forms. These diagrams contain many repetitions of phase portraits and we show that these are due to many symmetries under the group action. To retain the essence of the dynamics we finally construct the quotient spaces under the action of the group G = Aff(2, ℝ) × ℝ* of affine transformations and time homotheties and we place the phase portraits in these quotient spaces. The final diagrams retain only the necessary information to capture the dynamics under the motion in the parameter space as well as under this group action. We also present here necessary and sufficient conditions for an affine line to be invariant of multiplicity k for a quadratic system.

Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation

2013 ◽  
Vol 444-445 ◽  
pp. 791-795
Author(s):  
Yi Xiang Geng ◽  
Han Ze Liu
Keyword(s):  
Chaotic Behavior ◽  
Melnikov Method ◽  
Harmonic Excitation ◽  
Phase Portraits ◽  
Pipe Conveying Fluid ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Transition To Chaos ◽  
Subharmonic Bifurcations ◽  
Conveying Fluid

The subharmonic and chaotic behavior of a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. Melnikov method is applied for the system, and Melnikov criterions for subharmonic and homoclinic bifurcations are obtained analytically. The numerical simulations (including bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincare map) confirm the analytical predictions and exhibit the complicated dynamical behaviors.

Generating Multiple Chaotic Attractors from Sprott B System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650177 ◽  
Author(s):  
Qiang Lai ◽  
Shiming Chen
Keyword(s):  
Lyapunov Exponent ◽  
Function Method ◽  
Polynomial Function ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Phenomenon ◽  
Bifurcation Diagrams ◽  
Initial Values ◽  
Index 2 ◽  
Lyapunov Exponent Spectrum

Multiple chaotic attractors, implying several independent chaotic attractors generated simultaneously in a system from different initial values, are a very interesting and important nonlinear phenomenon, but there are few studies that have previously addressed it to our best knowledge. In this paper, we propose a polynomial function method for generating multiple chaotic attractors from the Sprott B system. The polynomial function extends the number of index-2 saddle foci, which determines the emergence of multiple chaotic attractors in the system. The analysis of the equilibria is presented. Two coexisting chaotic attractors, three coexisting chaotic attractors and four coexisting chaotic attractors are investigated for verifying the effectiveness of the method. The chaotic characteristics of the attractors are shown by bifurcation diagrams, Lyapunov exponent spectrum and phase portraits.

THE GENERATION AND ANALYSIS OF A NEW FOUR-DIMENSIONAL HYPERCHAOTIC SYSTEM

2007 ◽  
Vol 18 (06) ◽  
pp. 1013-1024 ◽  
Author(s):  
JIEZHI WANG ◽  
ZENGQIANG CHEN ◽  
ZHUZHI YUAN
Keyword(s):  
Lyapunov Exponent ◽  
Cross Product ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Bifurcation Diagrams ◽  
Dynamic Behaviors ◽  
System Parameters ◽  
Product Term ◽  
Two Parameters ◽  
Cross Product Term

A new four-dimensional continuous autonomous hyperchaotic system is considered. It possesses two parameters, and each equation of it has one quadratic cross product term. Some basic properties of it are studied. The dynamic behaviors of it are analyzed by the Lyapunov exponent (LE) spectrum, bifurcation diagrams, phase portraits, and Poincaré sections. The system has larger hyperchaotic region. When it is hyperchaotic, the two positive LE are both large and they are both larger than 1 if the system parameters are taken appropriately.

scholarly journals Computational Analysis and Bifurcation of Regular and Chaotic Ca2+ Oscillations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3324
Author(s):  
Xinxin Qie ◽  
Quanbao Ji
Keyword(s):  
Numerical Simulation ◽  
Center Manifold ◽  
Computational Analysis ◽  
System Model ◽  
Phase Portraits ◽  
Bifurcation Parameter ◽  
Bifurcation Diagrams ◽  
Saddle Node Bifurcation ◽  
The Stability ◽  
Torus Bifurcation

This study investigated the stability and bifurcation of a nonlinear system model developed by Marhl et al. based on the total Ca2+ concentration among three different Ca2+ stores. In this study, qualitative theories of center manifold and bifurcation were used to analyze the stability of equilibria. The bifurcation parameter drove the system to undergo two supercritical bifurcations. It was hypothesized that the appearance and disappearance of Ca2+ oscillations are driven by them. At the same time, saddle-node bifurcation and torus bifurcation were also found in the process of exploring bifurcation. Finally, numerical simulation was carried out to determine the validity of the proposed approach by drawing bifurcation diagrams, time series, phase portraits, etc.

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