Total Amplitude Control Research Articles

Dynamic Analysis of New Chaotic System with Five Scroll and Two Scroll Attractors: Offset Boosting and Total Amplitude Control, Adaptive Synchronization

Dynamic Analysis of New Chaotic System with Five Scroll and Two Scroll Attractors: Offset Boosting and Total Amplitude Control, Adaptive Synchronization

Dynamical analysis of a novel memristor-type chaotic map

As a unique nonlinear component, the discrete memristor, with its simple structure, is associated with the ability to lead to excellent chaotic performance in the construction of chaotic systems. This characteristic has elevated the discrete memristor to a hot topic in the field of chaos. This paper introduces a cosine hyperchaotic map. Numerical simulations reveal its rich dynamical behaviors. The chaotic map exhibits diverse chaotic control models, including partial amplitude control, total amplitude control, initial boosting, and parameter-offset boosting, with dynamical distribution diagrams plotted for amplitude control to quantify the range of amplitude modulation. Additionally, a localized boosting free region is identified, which exhibits extreme sensitivity to initial values. Dual offset parameters are introduced to control this localized boosting free region, enhancing the flexibility of the system. Finally, the map is implemented on STM32 to validate the numerical simulation results.

Attractor Merging and Amplitude Control of Hyperchaos in a Self-Reproducing Memristive Map

Memristor-type feedback provides a unique passage for chaos produced with easy control. In this work, a novel memristive map with amplitude control and coexisting hyperchaotic attractors is designed, in which two nonbifurcation parameters are extracted for partial amplitude control crossing the origin and total amplitude control. Attractor splitting and attractor merging are captured, which lead to five regimes of attractor self-reproducing. In this case, double-cavity attractors extend in the direction of 0[Formula: see text], 45[Formula: see text], 90[Formula: see text] in negative [Formula: see text]-axis, 90[Formula: see text] in positive [Formula: see text]-axis, 135[Formula: see text] in [Formula: see text]-axis forming a specific wall of self-reproduction. Furthermore, the FPGA-based hardware implementation is carried out showing consistent results with numerical simulation. Finally, a high-security chaotic encryption scheme is proposed for the orthogonal frequency division multiplexing transmission system, where the power division multiplexing technique and two-dimensional region joint encryption are effectively utilized. The security of the transmitted information is improved by the various coexisting attractors and nonbifurcation amplitude controllers.

Adjustable symmetry on the dynamics of a new chaotic system with cyclic symmetry: theoretical study, control and experimental investigation

In this study, we propose a new chaotic autonomous system with adjustable cyclic and central symmetries. The new 3D system, with rich dynamics, is constructed based on the Thomas model. A detailed study of the nonlinear dynamics arising from the model allows us to reveal complex behaviors of different phenomena such as hysteresis dynamics, offset boosting, total amplitude control, and coexistence of several homogeneous and heterogeneous attractors in both regimes (symmetric and asymmetric). The control of multistability of the new cyclic system is studied by following the technique of linear augmentation. An analog electronic version of the model is designed and then simulated using the Pspice software. Moreover, a physical implementation using the arduino microcontroller makes it possible to validate the results of the theoretical analysis.

Yet New Extreme Multistable Chaotic System

The upsurge of discovering complex dynamics in simple chaotic systems is spring up in academia. This essay is devoted to investigating extreme multistability in a simple chaotic system. Here, only six terms with one nonlinearity form the mathematical model of this system and brings it infinitely many unstable equilibria. The unstable equilibria make the system possess the ability to yield extreme multistability, including various types of chaotic and periodic attractors. The dynamic behaviors, e.g. extreme multistability and total amplitude control are numerically studied. To verify the proposed system’s physical existence, an analog circuit and implementation utilizing the microcontroller is devised as well, where their outcomes perfectly matched with those of simulations.

Dynamical Analysis and Offset Boosting in a 4-Dimensional Quintic Chaotic Oscillator with Circulant Connection of Space Variables

In recent years, much energy has been devoted to the study of chaotic models with specific features particularly those with cyclic connection of the variables. Previous ones provide multistability, amplitude control, and so on. Concerning the first phenomenon, models with ring connection of variables presented a coexistence of up to twelve disconnected attractors. In order to emphasize the complexity of circulant chaotic oscillators and their use in the engineering domain, a quintic chaotic model with cyclic connection of variables is considered and studied, which has complex equilibria located on the line x = y = z = w . Therefore, it experiences, amongst other, the phenomenon of offset boosting obtained by introducing four constants into the equations of the model, which has not be done in the past. Multistability is also revealed and the coexistence of eight and sixteen attractors is demonstrated using phase portraits. The system’s dynamics has been investigated considering its two parameters. Nonlinear dynamical tools such as bifurcation diagrams, phase portraits, time evolutions, two-parameter diagram, and Lyapunov exponents help to highlight the important phenomena encountered. The numerical results are confirmed using PSpice and particularly show the double-band chaotic attractor. Moreover, total amplitude control (TAC) is shown, proving that our oscillator can be used as an attenuator or amplifier in the engineering domain. The method of adaptive synchronization has been applied to the considered oscillator to emphasize the possible implication into the secure of communication systems.

A modified Rössler prototype-4 system based on Chua’s diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation

Abstract Since the introduction of chaos theory, the design of simple chaotic systems exhibiting complex dynamics has always been a hot research topic. Multistability and multiscroll generation are studied and applied in several domains like cryptography and engineering. This paper aims to construct a new three-dimensional chaotic system with up to eight coexisting attractors, inspired from one of the first prototype equations introduced by Rossler in 1976. The proposed system is multiplier-free, variable boostable and exclusively based on the Chua’s diode nonlinearity. The use of familiar tools such as bifurcation diagrams, Lyapunov exponents spectra, basins of attraction, frequency power spectra as well as Poincare map help to demonstrate its richer and complex dynamics. Chaos, antimonotonicity, total amplitude control, multistability as well as the multiscroll generation are investigated. Finally, an FPGA-based implementation is presented to confirm its feasibility.

Study of Amplitude Control and Dynamical Behaviors of a Memristive Band Pass Filter Circuit

The existence of a partial and total amplitude control in a band pass filter circuit with a memristor is explained theoretically and confirmed in simulations. A linear change of coordinates is derived to develop a simple three-parameter model of the circuit. Dynamical phenomena observed in the circuit are analyzed.

Linear synchronization and circuit implementation of chaotic system with complete amplitude control * *Project supported by the Startup Foundation for Introducing Talent of Nanjing University of Information Science & Technology, China (Grant No. 2016205), the Natural Science Foundation of the Jiangsu Higher Education Institutions of Jiangsu Province, China (Grant No. 16KJB120004), the Priority Academic Program Development of Jiangsu Higher Education

Although chaotic signals are considered to have great potential applications in radar and communication engineering, their broadband spectrum makes it difficult to design an applicable amplifier or an attenuator for amplitude conditioning. Moreover, the transformation between a unipolar signal and a bipolar signal is often required. In this paper, a more intelligent hardware implementation based on field programmable analog array (FPAA) is constructed for chaotic systems with complete amplitude control. Firstly, two chaotic systems with complete amplitude control are introduced, one of which has the property of offset boosting with total amplitude control, while the other has offset boosting and a parameter for partial control. Both cases can achieve complete amplitude control including amplitude rescaling and offset boosting. Secondly, linear synchronization is established based on the special structure of chaotic system. Finally, experimental circuits are constructed on an FPAA where the predicted amplitude control is realized through only two independent configurable analog module (CAM) gain values.

Constructing Chaotic Systems with Total Amplitude Control

A general method is introduced for controlling the amplitude of the variables in chaotic systems by modifying the degree of one or more of the terms in the governing equations. The method is applied to the Sprott B system as an example to show its flexibility and generality. The method may introduce infinite lines of equilibrium points, which influence the dynamics in the neighborhood of the equilibria and reorganize the basins of attraction, altering the multistability. However, the isolated equilibrium points of the original system and their stability are retained with their basic properties. Electrical circuit implementation shows the convenience of amplitude control, and the resulting oscillations agree well with results from simulation.

Multistability in symmetric chaotic systems

Chaotic dynamical systems that are symmetric provide the possibility of multistability as well as an independent amplitude control parameter.The Rossler system is used as a candidate for demonstrating the symmetry construction since it is an asymmetric system with a single-scroll attractor. Through the design of symmetric Rossler systems, a symmetric pair of coexisting strange attractors are produced, along with the desired partial or total amplitude control.

Linearization of the Lorenz system

A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system.