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.

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

Stability of the Jeffcott Rotor with Local Rubbing

2011 ◽  
Vol 55-57 ◽  
pp. 933-936
Author(s):  
He Li ◽  
Xiao Zhe Chen ◽  
Bang Chun Wen
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Stability Condition ◽  
Center Manifold ◽  
System Stability ◽  
Double Zero ◽  
Stability And Bifurcation ◽  
Jeffcott Rotor ◽  
The Stability ◽  
Bifurcation Behavior

The stability and bifurcation behavior of Jeffcott rotor with local rubbing are investigated in terms of Hartman-Grobman theorem in this paper. The case with double zero real part of eigenvalues is analyzed by means of the theory of center manifold and n-dimension Hopf bifurcation. Along with discussion for the effects of parameters on system stability and bifurcation behavior, numerical simulation of rotor locus is conducted and the stability condition is derived.

scholarly journals Dynamics Analysis and Control of a Five-Term Fractional-Order System

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Li-xin Yang ◽  
Xiao-jun Liu
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Phase Portraits ◽  
Order System ◽  
Bifurcation Diagrams ◽  
Compound Structure ◽  
Dynamical Properties ◽  
The Stability ◽  
And Control

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.

scholarly journals Effective Control and Bifurcation Analysis in a Chaotic System with Distributed Delay Feedback

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Wei Tan ◽  
Jianguo Gao ◽  
Wenjun Fan
Keyword(s):  
Hopf Bifurcation ◽  
Chaotic System ◽  
Center Manifold ◽  
Distributed Delay ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Bifurcation Parameter ◽  
Normal Form Theorem ◽  
The Stability ◽  
Variation Tendency

We discuss the dynamic behavior of a new Lorenz-like chaotic system with distributed delayed feedback by the qualitative analysis and numerical simulations. It is verified that the equilibria are locally asymptotically stable whenα∈(0,α0)and unstable whenα∈(α0,∞); Hopf bifurcation occurs whenαcrosses a critical valueα0by choosingαas a bifurcation parameter. Meanwhile, the explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by normal form theorem and center manifold argument. Furthermore, regardingαas a bifurcation parameter, we explore variation tendency of the dynamics behavior of a chaotic system with the increase of the parameter valueα.

Bifurcation Analysis of a One-Prey and Two-Predators Model with Additional Food and Harvesting Subject to Toxicity

2021 ◽  
Vol 31 (06) ◽  
pp. 2150089
Author(s):  
Biruk Tafesse Mulugeta ◽  
Liping Yu ◽  
Jingli Ren
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Additional Food ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Generalized Hopf Bifurcation ◽  
Form Theory

In this paper, a three-dimensional one-prey and two-predators model, with additional food and harvesting in the presence of toxicity is proposed. Additional food is being provided to one predator. The dynamics and bifurcations of the system are investigated using center manifold theorem, normal form theory and Sotomayor’s theorem. It is proved that the system undergoes transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, generalized Hopf bifurcation, Bogdanov–Takens bifurcation and cusp bifurcation with respect to different parameters. Bifurcation diagrams of the system with respect to toxic effect and harvesting effect are illustrated. The phase portraits and solution curves are also presented to verify the dynamic behavior. The results show that the combined effect of the factors has the power of transforming simple ecosystems into complex ecosystems.

Analysis of a Delayed Eco-Epidemiological Pest–Plant Model with Infected Pest

2019 ◽  
Vol 14 (03) ◽  
pp. 141-170 ◽  
Author(s):  
Ashok Mondal ◽  
A. K. Pal ◽  
G. P. Samanta
Keyword(s):  
Numerical Simulation ◽  
Ecological Model ◽  
Well Posedness ◽  
Type Ii ◽  
Bifurcation Parameter ◽  
Pest Population ◽  
Plant Model ◽  
Interior Equilibrium ◽  
The Stability ◽  
Plant Ecological

This work describes a delayed pest–plant ecological model with infection in the pest population. The interactions between plant and susceptible pest and also between susceptible and infected pest are taken as Holling type II responses. Well-posedness of the system has been discussed. Stability analysis of all equilibria has been performed. The effect of time-delay has been studied, where the delay may be regarded as the incubation period of the infected pest. Existence of a Hopf-bifurcation around interior equilibrium has been established by considering the amount of delay as bifurcation parameter. The length of delay is estimated for which the stability continues to hold. Numerical simulation with a hypothetical set of data has been presented to validate analytical findings.

scholarly journals Parameter-Independent Dynamical Behaviors in Memristor-Based Wien-Bridge Oscillator

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ning Wang ◽  
Bocheng Bao ◽  
Tao Jiang ◽  
Mo Chen ◽  
Quan Xu
Keyword(s):  
Chaotic Attractor ◽  
Initial Conditions ◽  
System Model ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Chaotic Oscillator ◽  
Initial Condition ◽  
Bifurcation Diagrams ◽  
System Parameters ◽  
Dynamical Behaviors

This paper presents a novel memristor-based Wien-bridge oscillator and investigates its parameter-independent dynamical behaviors. The newly proposed memristive chaotic oscillator is constructed by linearly coupling a nonlinear active filter composed of memristor and capacitor to a Wien-bridge oscillator. For a set of circuit parameters, phase portraits of a double-scroll chaotic attractor are obtained by numerical simulations and then validated by hardware experiments. With a dimensionless system model and the determined system parameters, the initial condition-dependent dynamical behaviors are explored through bifurcation diagrams, Lyapunov exponents, and phase portraits, upon which the coexisting infinitely many attractors and transient chaos related to initial conditions are perfectly offered. These results are well verified by PSIM circuit simulations.

Hopf Bifurcation Analysis for a Novel Hyperchaotic System

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Kejun Zhuang
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Normal Form ◽  
Local Stability ◽  
Center Manifold ◽  
Hyperchaotic System ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
The Stability

The paper mainly focuses on a novel hyperchaotic system. The local stability of equilibrium is analyzed and existence of Hopf bifurcation is established. Moreover, formulas for determining the stability and direction of bifurcating periodic solutions are derived by center manifold theorem and normal form theory. Finally, numerical simulation is given to illustrate the theoretical analysis.

Coexisting Multi-Dynamics of a Physical SBT Memristor-Based Chaotic Circuit

2020 ◽  
Vol 30 (11) ◽  
pp. 2030043
Author(s):  
Gang Dou ◽  
Hai Yang ◽  
Zhenhao Gao ◽  
Peng Li ◽  
Minglong Dou ◽  
...  
Keyword(s):  
Equilibrium Point ◽  
Lyapunov Exponents ◽  
Phase Portraits ◽  
Circuit Parameter ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Initial State ◽  
Stable Point ◽  
The Stability ◽  
Physical Formula

This paper presents a new physical [Formula: see text] (SBT) memristor-based chaotic circuit. The equilibrium point and the stability of the chaotic circuit are analyzed theoretically. This circuit system exhibits multiple dynamics such as stable point, periodic cycle and chaos by means of Lyapunov exponents spectra, bifurcation diagrams, Poincaré maps and phase portraits, when the initial state or the circuit parameter changes. Specially, the circuit system exhibits coexisting multi-dynamics. This study provides insightful guidance for the design and analysis of physical memristor-based circuits.

Hopf bifurcation analysis in a turbidostat model with Beddington–DeAngelis functional response and discrete delay

2017 ◽  
Vol 10 (05) ◽  
pp. 1750061
Author(s):  
Yong Yao ◽  
Zuxiong Li ◽  
Huili Xiang ◽  
Hailing Wang ◽  
Zhijun Liu
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Functional Response ◽  
Center Manifold ◽  
Critical Value ◽  
Hopf Bifurcations ◽  
Bifurcation Parameter ◽  
Discrete Delay ◽  
Center Manifold Theorem ◽  
The Stability

In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington–DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results.

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