Pdf on the dynamics of new 4d lorenztype chaos systems. The stability results are established using pi proportional integral switching surface and lyapunov stability theory for hybrid synchronization scheme. This paper discusses the complex dynamics of a new fourdimensional continuoustime autonomous hyperchaotic lorenz type system. Thus, the master system is described by the hyperchaotic lorenz dynamics 1214 2 12 312 3 4 4 x ax x x x xx rx x xxxbx xxxdx. So at present the controlling of the hyperchaotic system simply and effectively is a frontier topic of nonlinear science. Periodic, quasiperiodic, chaotic and hyper chaotic behavior of parametric perturbated lorenz map is discussed bymeans of bifurcation diagram. We characterize the zerohopf bifurcation at the singular points of a parameter codimension four hyperchaotic lorenz system. Design of a sinusoidally driven lorenz system lorenz system is described as follows. Complexity analysis and dsp implementation of the fractional. This hyperchaotic system is not only visualized by computer simulation but also verified.
This hyperchaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. In this paper, based on the classical lorenz system, a new lorenz. Complex dynamic behaviors of the complex lorenz system core. By further dimension extension, a new 4d hyperchaotic system with seven terms is constructed. Complexity of this system versus parameters are analyzed by lces, bifurcation diagrams, phase portraits, complexity algorithms. This hyperchaotic complex system is constructed by adding a linear controller to the second equation of the chaotic complex lorenz system. Not topologically conjugate to the lorenz attractor. Recently, a socalled hyperchaotic lorentz system was introduced. Antisynchronization errors,, in hyperchaotic lorenz system and hyperchaotic lu system shown in order figure 7 until figure 10. The alternating between complete synchronization and. A new fourdimensional hyperchaotic lorenz system and its adaptive control.
The adaptive hybrid synchronization between two identical systems hyperchaotic chen system and different systems hyperchaotic lorenz and hyperchaotic systems are taken as two illustrative examples to show the effectiveness of the proposed method. Projective synchronization of a new hyperchaotic lorenz system. Comparison of the lorenz like hyperchaotic systems. For the hyperchaotic lorenz 4d system the extra parameter. Dynamics of a hyperchaotic lorenz system international. Hybrid adaptive synchronization of hyperchaotic systems with. The time response of,, states for drive system hyperchaotic lorenz and the response system hyperchaotic lu via active generalized backstepping method shown in order figure 3 until figure 6. This paper introduces a new hyperchaotic system not derived from previous 3d. In this paper, we investigate the dynamics of the lorenz system, linearly extended into one additional dimension. This paper presents a novel unified hyperchaotic system that contains the hyperchaotic lorenz system and the hyperchaotic chen system as two dual systems at the two extremes of its parameter spectrum. After an exhaustive research on a new 4d lorenz type hyperchaotic system and a coupled dynamo chaotic system, we obtain the bounds of the new 4d lorenz. In this paper, we further investigate its synchronization and circuit implementation. In this section, the fractionalorder hyperchaotic lorenz system is presented, and a novel image encryption scheme is described in detail. Pdf a novel hyperchaotic system and its control researchgate.
International journal on computer science and engineering ijcse. By introducing a sinusoidal function controller into the rst. Pdf this paper is concerned with the projective synchronization problem for a class of 6d nonlinear dynamical system which is called hyperchaotic. The hyperchaotic lorenz system is one of the paradigms of the fourdimensional hyperchaotic systems discovered by g. Research article control and synchronization of chaotic and. Design and implementation of grid multiwing hyperchaotic. The alternating between complete synchronization and hybrid synchronization of hyperchaotic lorenz 1179. A hyperchaos generated from lorenz system sciencedirect. Hybrid adaptive synchronization of hyperchaotic systems. The local dynamics, such as the stability, pitchfork bifurcation, and hopf bifurcation at equilibria of this hyperchaotic system are analyzed by using the parameterdependent center manifold theory and the normal form theory. Many hyperchaotic systemsbased onan extension of the famous lorenz 1963 system have been proposed li et al. The systems will never get synchronized if walone is the. A new image encryption algorithm based on the fractional.
This paper presents a fourdimension hyperchaotic lorenz system, obtained by adding a nonlinear controller to lorenz chaotic system. Synchronization of a new hyperchaotic lorenz system. Generalized projective synchronization of chaotic systems. In section 3, the corresponding chaotic and hyperchaotic circuits are designed with diodes for the signal switch. Global synchronization of the new hyperchaotic systems can be achieved. Function projective synchronization of discretetime chaotic. However, these lorenz like systems have more than seven terms and more than two parameters, and thus it is. Also, the approach may be suitable for practical implementationin some real systems. Pdf synchronization and control of hyperchaotic complex. Ps with both identical and different scaling factors between two hyperchaotic lorenz systems are realized. Generalized projective synchronization for different.
A new hyperchaotic lorenz system has been proposed recently. A new fourdimensional hyperchaotic lorenz system and its. Hyperchaos, adaptive control and synchronization of a novel 5d. Chaos synchronization of a class 6d hyperchaotic lorenz system. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. A new hyperchaotic system and its circuit implementation, elsevier,volume 1511, system and its circuit implementation, elsevier. Research article control and synchronization of chaotic. Pdf, application of hyperchaotic lorenz system for.
In this letter, for the latest hyperchaotic lorenz system, four feedback. For convenience, the drive hyperchaotic lorenz system with timedelay is. Fractionalorder lorenz hyperchaotic system by introducing a nonlinear quadratic controller uto the second equation of lorenz system, a four dimensional dynamic system is obtained 28 8. Pdf complexity analysis and dsp implementation of the. This paper is devoted to investigate the tracking control and generalized synchronization of the hyperchaotic lorenz stenflo system using the tracking model and the feedback control scheme. By designing an active sliding mode controller and choosing proper control parameters, the master and slave systems are synchronized. More and more attention has been payed to the hyperchaotic system for the huge potential applications of hyperchaotic system such as secure communication and more complex structure than chaotic system. Zerohopf bifurcation in a hyperchaotic lorenz system. Coexisting hidden attractors in a 4d simplified lorenz system. Chua circuit 4, the hyperchaotic lorenz system 5, the hyperchaotic chen system 6 and the hyperchaotic lu system 7. A sinusoidally driven lorenz system and circuit implementation. Lorenz system of differential equations is used as a source for carriers of the chaotic spectrum. Zerohopf bifurcation in a hyperchaotic lorenz system core. Bridge between the hyperchaotic lorenz system and the.
Mathematical and computational applications article chaos synchronization for hyperchaotic lorenz type system. A symmetric controllable hyperchaotic hidden attractor mdpi. Although the globally attractive sets of a hyperchaotic system have important applications in the fields of engineering, science, and technology, it is often a difficult task for the researchers to obtain the globally attractive set of the hyperchaotic systems due to the complexity of the hyperchaotic systems. These systems also detect the weak signal with low signal to noise ratio snr. Noticeably, based on two drive complex systems and one response complex system with different dimensions, we propose generalized combination complex. Bifurcation analysis is used to demonstrate chaotic and hyperchaotic behaviors of our new systems. Research article a sinusoidally driven lorenz system and. It is generated by controlling a generalized lorenz system to hyperchaotic by introducing a linear state feedback controller to the second equation of generalize lorenz system. New chaotic system and its hyperchaos generation ieee xplore. In order to solve the chaos synchronization problem for a hyperchaotic lorenz type system, we propose an observer based synchronization under a masterslave configuration.
This work is devoted to investigating the hybrid synchronization phenomenon of two identical hyperchaotic lorenz timedelay systems with different initial conditions, and a simple coexistence of an. An audio encryption scheme based on fast walsh hadamard. We remark that not all these hyperchaotic lorenz systems coincide, as they can vary in one or two terms. Hyperchaotic systems have applications in multiple areas of science and engineering. Finally, in section 7 the conclusion of the paper is given. Inverse projective synchronization between two different. The 5d novel hyperchaotic lorenz system proposed in this work. In this paper, a new hyperchaotic complex system is presented and its dynamical properties are discussed by phase portraits, bifurcation diagrams, and the lyapunov exponents spectra. Dynamics of a hyperchaotic lorenztype system springer for. Systems description in this work, two nonlinear systems are studied, namely, chaotic lorenz system and hyperchaotic lorenz system. Diffusive synchronization of hyperchaotic lorenz systems. A weak signal detection application based on hyperchaotic lorenz. Chaos synchronization for hyperchaotic lorenztype system via. Onedimensional signalcompression by fwht is also discussed.
Ps was observed for dynamical systems with real variables 10,24,35, where the drive and response systems could be synchronized up to a scaling factor. Chaos synchronization of a class 6d hyperchaotic lorenz. The alternating between complete synchronization and hybrid. Numerical simulations show that the new system s behavior can be convergent, divergent, periodic, chaotic and hyperchaotic when the parameter varies. This study investigates the hybrid synchronization of hyperchaotic lorenz and chen systems via adaptive control. Simulation results obtained from matlabsimulink program verify the studied. Request pdf hyperchaotic lorenz system this paper presents a fourdimensional hyperchaotic lorenz system, obtained by adding a nonlinear controller to lorenz chaotic system. Pdf in this paper, a new hyperchaotic system is constructed via state feedback. Of particular interest are the observations that the hyperchaotic system has a hyperchaotic attractor with three positive lyapunov exponents under a unique equilibrium.
Pdf dynamics and synchronization of new hyperchaotic. Design and fpga implementation of a wireless hyperchaotic. Therefore, we will study the globally attractive set of a generalized hyperchaotic. The hyperchaotic lorenz system is studied by bifurcation diagram, lyapunov exponents spectrum and phase diagram. In recent years, due to its characteristics of high capacity, high security and high ef.
Chaos synchronization of a class 6d hyperchaotic lorenz system ahmed s. A simple electrical circuit described by the lorenz 4d equations is proposed. By linearizing the threedimensional generalized lorenz system family at their two symmetric equilibria. Abstract the aim of this paper is to introduce a new hyperchaotic complex lorenz system.
Fractionalorder hyperchaotic lorenz system the fractionalorder hyperchaotic lorenz system is used in the encryption algorithm, which is described by 8. This paper initiates a systematic methodology for generating various grid multiwing hyperchaotic attractors by switching control and constructing superheteroclinic loops from the piecewise linear hyperchaotic lorenz system family. Lyapunov characteristic exponents lces of this system are calculated according to this deduced discrete map. Generalized combination complex synchronization of new. We suppress the chaos to unstable equilibrium via three feedback methods, and we achieve three globally generalized synchronization controls. Hybrid synchronization phenomenon in two coupled delay. Chlouverakis and sprott 10 proposed what may be the algebraically simplest hyperchaotic snap system. Global chaos synchronization of hyperchaotic lorenz and. A theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a. Interpolates between lorenz like and chenlike behavior. The new system is a 7dimensional continuous real autonomous hyperchaotic system.
The fractionalorder hyperchaotic lorenz system is solved as a discrete map by applying the adomian decomposition method adm. Synchronisation of the hyperchaotic complex lorenz system. This paper mainly investigates a novel inverse projective synchronization between two different fractionalorder hyperchaotic systems, that is, the fractionalorder hyperchaotic lorenz system and the fractionalorder hyperchaotic chen system. This hyper chaotic system has very simple algebraic structure but can exhibit complex dynamical behaviors. Control and synchronization of hyperchaotic states in. There are also some chaotic systems of great significance that are closely related to the lorenz system, examples of which are the chen system and the lu system. A new 5d hyperchaotic system based on modified generalized. Using averaging theory, we find sufficient conditions so that at the bifurcation points two periodic solutions emerge and describe the stability of these orbits. Hyperchaotic lu system is considered as master and hyperchaotic bao system as slave system. Alobeidi saad fawzi alazzawi department of mathematics, college of computer sciences and mathematics, university of mosul, mosul, iraq. Dynamical systems where the main variables are complex appear in many important fields of physics and communications. We assume that the parameters of the master and slave systems are unknown dr. Chaotic control and generalized synchronization for a. M athscinet presently lists 24 papers on hyperchaotic lorenz systems.
This system has hyperchaotic attractors and quasiperiodic solutions with three. Projective synchronization of system 1 in this section we study the ps of hyperchaotic attractors of complex lorenz system 1 using an active control technique based on lyapunov function. Mathematical and computational applications article chaos synchronization for hyperchaotic lorenz type system via. This system has hyperchaotic attractors and quasiperiodic solutions with three zero. Zerohopf bifurcations in a hyperchaotic lorenz system ii 1. The synchronizing properties of two diffusively coupled hyperchaotic lorenz 4d systems are investigated by calculating the transverse lyapunov exponents and by observing the phase space trajectories near the synchronization hyperplane. Synchronization of coupled nonidentical fractionalorder. Another approach is developed for generating twowing hyperchaotic attractor, fourwing chaotic attractor, and high periodic orbits such as period14 from a. Furthermore, synchronizing fractionalorder hyperchaotic lorenz system and fractionalorder hyperchaotic chen system is performed to show the effectiveness of the proposed controller.
Moreover numerical simulations are used to verify the e. The new system is hyperchaotic over almost the whole range of the system parameter and continuously transfers from the hyperchaotic lorenz system to the hyperchaotic chen system. In this note, by using the theory of bifurcation and lyapunov function, one performs a qualitative analysis on a novel fourdimensional unified hyperchaotic lorenz type system uhlts, including stability, pitchfork bifurcation, hopf bifurcation, singularly degenerate heteroclinic cycle, ultimate bound estimation, global exponential attractive set, heteroclinic orbit and so on. Synchronization and control of hyperchaotic complex lorenz system. Dynamics of a hyperchaotic lorenztype system springer. Theoretical analysis and numerical simulations are shown to verify the results. Chen, design and implementation of grid multiwing hyperchaotic lorenz system family via switching control and constructing superheteroclinic loops, ieee.
A general sufficient condition for ps in a certain class of chaotic hyperchaotic system with uncertainties is obtained by using adaptive control. Lorenz system has been extensively studied in the field of chaos theory and. Little seems to be known about the multistable hyperchaotic systems. Bifurcations, ultimate boundedness and singular orbits in. In figure 1, the two largest tle for singlevariable coupling are plotted as a function of k,forr 30. Antisynchronization of the hyperchaotic lorenz systems by. The fractional lyapunov dimension of the hyperchaotic attractors of these systems is calculated.
The system is hyperchaotic in a wide range of parameters. This letter mainly concerns projective synchronization ps of a new hyperchaotic lorenz system. A new hyperchaotic attractor with complex patterns arxiv. Comparison of feedback control methods for a hyperchaotic. Explicitly, researchers derive new results for the hybrid chaos synchronization of identical hyperchaotic lorenz systems, identical hyperchaotic chen systems and nonidentical hyperchaotic lorenz and chen systems.
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