scholarly journals A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design

2021 ◽  
Vol 11 (4) ◽  
pp. 2941
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Irene M. Moroz ◽  
Babatunde Idowu ◽  
Mohamad Afendee Mohamed ◽  
...  
Keyword(s):  
Circuit Design ◽  
Qualitative Agreement ◽  
Research Study ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Backstepping Technique ◽  
Good Qualitative Agreement ◽  
Jerk System ◽  
Jerk Dynamics

<span>This paper announces a new three-dimensional chaotic jerk system with two saddle-focus equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. By modifying the Genesio-Tesi jerk dynamics (1992), a new jerk system is derived in this research study. The new jerk model is equipped with multistability and dissipative chaos with two saddle-foci equilibrium points. By invoking backstepping technique, new results for synchronizing chaos between the proposed jerk models are successfully yielded. MultiSim software is used to implement a circuit model for the new jerk dynamics. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM results</span>

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.

THE CUSP–HOPF BIFURCATION

2007 ◽  
Vol 17 (08) ◽  
pp. 2547-2570 ◽  
Author(s):  
J. HARLIM ◽  
W. F. LANGFORD
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Invariant Tori ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Planar System ◽  
Bursting Oscillations ◽  
Codimension Two ◽  
Truncated Normal ◽  
Comprehensive Study

The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold. It is based on truncated normal form equations, which have a phase-shift symmetry yielding a further reduction to a planar system. Bifurcation varieties and phase portraits are presented. The phenomena include all four cases that occur in the codimension-two fold–Hopf bifurcation, in addition to bistability involving equilibria, limit cycles or invariant tori, and a fold–heteroclinic bifurcation that leads to bursting oscillations. Uniqueness of the torus family is established locally. Numerical simulations confirm the prediction from the bifurcation analysis of bursting oscillations that are similar in appearance to those that occur in the electrical behavior of neurons and other physical systems.

A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation

2018 ◽  
pp. 382-419 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Ahmad Taher Azar ◽  
Aceng Sambas ◽  
Shikha Singh ◽  
Kammogne Soup Tewa Alain ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Dissipative System ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Qualitative Properties ◽  
New Hyperchaotic System

This chapter announces a new four-dimensional hyperchaotic system having two positive Lyapunov exponents, a zero Lyapunov exponent, and a negative Lyapunov exponent. Since the sum of the Lyapunov exponents of the new hyperchaotic system is shown to be negative, it is a dissipative system. The phase portraits of the new hyperchaotic system are displayed with both two-dimensional and three-dimensional phase portraits. Next, the qualitative properties of the new hyperchaotic system are dealt with in detail. It is shown that the new hyperchaotic system has three unstable equilibrium points. Explicitly, it is shown that the equilibrium at the origin is a saddle-point, while the other two equilibrium points are saddle-focus equilibrium points. Thus, it is shown that all three equilibrium points of the new hyperchaotic system are unstable. Numerical simulations with MATLAB have been shown to validate and demonstrate all the new results derived in this chapter. Finally, a circuit design of the new hyperchaotic system is implemented in MultiSim to validate the theoretical model.

A Memristive Hyperchaotic Multiscroll Jerk System with Controllable Scroll Numbers

2017 ◽  
Vol 27 (06) ◽  
pp. 1750091 ◽  
Author(s):  
Chunhua Wang ◽  
Hu Xia ◽  
Ling Zhou
Keyword(s):  
Three Dimensional ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Complex Dynamic ◽  
Coexisting Attractors ◽  
Circuit Element ◽  
Circuit Structure ◽  
Jerk System ◽  
New System ◽  
System Phase

A memristor is the fourth circuit element, which has wide applications in chaos generation. In this paper, a four-dimensional hyperchaotic jerk system based on a memristor is proposed, where the scroll number of the memristive jerk system is controllable. The new system is constructed by introducing one extra flux-controlled memristor into three-dimensional multiscroll jerk system. We can get different scroll attractors by varying the strength of memristor in this system without changing the circuit structure. Such a method for controlling the scroll number without changing the circuit structure is very important in designing the modern circuits and systems. The new memristive jerk system can exhibit a hyperchaotic attractor, which has more complex dynamic behavior. Furthermore, coexisting attractors are observed in the system. Phase portraits, dissipativity, equilibria, Lyapunov exponents and bifurcation diagrams are analyzed. Finally, the circuit implementation is carried out to verify the new system.

The Crystal Structure of Potassium Hydrogeniodate (V), KIO3•HIO3

1972 ◽  
Vol 50 (8) ◽  
pp. 1134-1143 ◽  
Author(s):  
G. Kemper ◽  
Aafje Vos ◽  
H. M. Rietveld
Keyword(s):  
Crystal Structure ◽  
Hydrogen Bonds ◽  
Single Crystal ◽  
Powder Diffraction ◽  
Qualitative Agreement ◽  
Three Dimensional ◽  
Neutron Powder Diffraction ◽  
X Ray Diffraction ◽  
Good Qualitative Agreement ◽  
X Ray

The crystal structure of KIO3•HIO3 has been determined by three-dimensional single crystal X-ray diffraction and by neutron powder diffraction. The crystallographic data are a = 7.025(2), b = 8.206(2), c = 21.839(5) Å, β = 97.98(2)°, space group P21/c, Z = 8 units KIO3•HIO3. The residual [Formula: see text] was 0.048 for 7516 independent X-ray reflections measured on a three-circle diffractometer with Zr-filtered Mo radiation. The results of the present study show good qualitative agreement with the structure recently determined by Chan and Einstein (7). The HIO3 and [Formula: see text] groups are pyramidal, the I—O(H) bonds vary from 1.898 to 1.939(4) Å and the I—O bonds from 1.786 to 1.827(4) Å, these lengths are not corrected for the effects of thermal motion. Strong O—I … O interactions and electrostatic attractions between K+ and Oδ− give slabs of thickness [Formula: see text] The slabs are connected by hydrogen bonds of 2.710 and 2.694 Å.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

Bursting Oscillations and Experimental Verification of a Rucklidge System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130023
Author(s):  
Zhijun Li ◽  
Siyuan Fang ◽  
Minglin Ma ◽  
Mengjiao Wang
Keyword(s):  
Electronic Devices ◽  
Pitchfork Bifurcation ◽  
Phase Portraits ◽  
Formation Mechanisms ◽  
Analysis Method ◽  
Good Qualitative Agreement ◽  
Bursting Oscillations ◽  
Real Time Measurement ◽  
Time Varying Parameter ◽  
Measurement Results

Bursting oscillations are ubiquitous in multi-time scale systems and have attracted widespread attention in recent years. However, research on experimental demonstration of the bursting oscillations induced by delayed bifurcation is very rarely reported. In this paper, a parametrically driven Rucklidge system is introduced and a distinct delayed behavior is observed when the time-varying parameter passes through the pitchfork bifurcation point. Different bursting patterns induced by such a delayed behavior are numerically investigated under different excitation amplitudes based on the fast–slow analysis method. Furthermore, in order to reproduce the bursting electronic signals and explore the underlying formation mechanisms experimentally, a real physical circuit of the parametrically driven Rucklidge system is developed by using off-the-shelf electronic devices. The real-time measurement results such as time series, phase portraits and transformed phase portraits are in good qualitative agreement with those obtained from the numerical computations. The experimental evidence to verify bursting oscillations induced by delayed pitchfork bifurcation is thus provided in this study.

scholarly journals Three-dimensional lattice logic circuits, Part I: Fundamentals

2005 ◽  
Vol 18 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Anas Al-Rabadi
Keyword(s):  
Circuit Design ◽  
Fault Localization ◽  
Three Dimensional ◽  
Logic Circuits ◽  
Logic Circuit ◽  
Device Performance ◽  
Important Class ◽  
Future Directions ◽  
Dimensional Lattice ◽  
Current Technology

Fundamentals of regular three-dimensional (3D) lattice circuits are introduced. Lattice circuits represent an important class of regular circuits that allow for local interconnections, predictable timing, fault localization, and self-repair. In addition, three-dimensional lattice circuits can be potentially well suited for future 3D technologies, such as nanotechnologies, where the intrinsic physical delay of the irregular and lengthy interconnections limits the device performance. Although the current technology does not offer a menu for the immediate physical implementation of the proposed three-dimensional circuits, this paper deals with three-dimensional logic circuit design from a fundamental and foundational level for a rather new possible future directions in designing digital logic circuits.

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