Bifurcations of fractionalorder diffusionless lorenz system. Control and synchronization of a new hyperchaotic system. Lorenz equations is preserved or removed, a new piecewise linear hyperchaotic system results with only signum and absolutevalue nonlinearities. Oct 21, 2011 a hyperchaotic attractor is typically defined as chaotic behavior with at least two positive lyapunov exponents.
Antisynchronization of the hyperchaotic lorenz systems by. Also, the approach may be suitable for practical implementationin some real systems. Hyperchaotic systems have applications in multiple areas of science and engineering. After that, chaotic systems have been researched extensively, such as the lu system 24, the chen system 5 and the rossler system 6. The appearance and also the characteristics of the new 4d attractor are utterly distinct from the other existing hyperchaotic systems 4d lorenzhaken system, 4d hyperchaotic chuas circuit, 4d hyperchaotic chen, etc. A novel hyperchaotic system with fractionalorder terms has been proposed in 14. Lorenz system of differential equations is used as a source for carriers of the chaotic spectrum.
International journal on computer science and engineering ijcse issn. Hyperchaotic attractor with multiple independent controllers. This hyperchaotic system is not only visualized by computer simulation but also verified with bifurcation analysis and realized with an electronic circuit. 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.
Pdf memristorbased lorenz hyperchaotic system and its. Recently, based on the lorenz system and state feedback control, a new 5d hyperchaotic system was reported by hu in 2009, and yang et al. Lyapunov characteristic exponents lces of this system are calculated according to this deduced discrete map. Zerohopf bifurcation in a hyperchaotic lorenz system lorena cidmontiel jaume llibre cristina stoica the date of receipt and acceptance should be inserted later abstract we characterize the zerohopf bifurcation at the singular points of a parameter codimension four hyperchaotic lorenz system. Hyperchaos and hyperchaos control of the sinusoidally forced. When considering a fivedimensional selfexciting homopolar disc dynamo, wei et al. Pdf, application of hyperchaotic lorenz system for. In mathematics, a chaotic map is a map evolution function that exhibits some sort of chaotic behavior. The fractionalorder hyperchaotic lorenz system is solved as a discrete map by applying the adomian decomposition method adm.
Chaos control and synchronization of a novel 5d hyperchaotic. Adomian decomposition method for a given fractionalorder chaotic system with the form of dq t0 xt fxt, where xt xt,yt,zt,utt are the state variables. The generalized projective synchronization of hyperchaotic. The hyperchaotic lorenz system 28,29 is described by. Hybrid adaptive synchronization of hyperchaotic systems. The systems will never get synchronized if walone is the. Numerical solution of the fractionalorder lorenz hyperchaotic system 2. Research article control and synchronization of chaotic. In this paper, we investigate the dynamics of the lorenz system, linearly extended into one additional dimension. Fractionalorder hyperchaotic lorenz system the fractionalorder hyperchaotic lorenz system is used in the encryption algorithm, which is described by 8. Dynamic analysis and circuit implementation of a new 4d.
A hyperchaos generated from lorenz system request pdf. Generalized projective synchronization for different. Furthermore, based on lyapunov stability theory, an adaptive controller is designed and the new 4d hyperchaotic lorenz system is controlled at equilibrium point. This approximation is a coupling of the navierstokes equations with thermal convection. Research article control and synchronization of chaotic and. Coexisting hidden attractors in a 4d simplified lorenz system. The original problem was a 2d problem considering the thermal convection between two parallel horizontal plates. Since hyperchaotic system has the characteristics of high capacity, high security and high ef. Based on the properties of a passive system, a passive controller is designed and the synchronization between two hyperchaotic lorenz systems under different. Adaptive synchronization for an uncertain new hyperchaotic.
The lorenz system 1 formulation 1 formulation the lorenz system was initially derived from a oberbeckboussinesq approximation. In this section, the fractionalorder hyperchaotic lorenz system is presented, and a novel image encryption scheme is described in detail. A theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a. Dynamical equations have seven terms without any quadratic or higher order polynomials and, to our knowledge, are the simplest hyperchaotic system. Pdf on the dynamics of new 4d lorenztype chaos systems. A sinusoidal function controller is introduced into a 3d autonomous lorenz system, so that the abovementioned various hyperchaotic attractors, chaotic attractors, and high periodic orbits. Based on lyapunov stability theory and adaptive synchronization method, an adaptive control law and a parameter update rule for unknown parameters are given for self synchronization of the hyperchaotic lorenz systems. Request pdf a hyperchaos generated from lorenz system this paper presents a fourdimension hyperchaotic lorenz system, obtained by adding a nonlinear. First of all, a hyperchaotic system is constructed by introducing two state variables into the lorenz chaotic system.
Chaotic control and generalized synchronization for a hyperchaotic lorenz stenflo system yinli, 1,2 yulinzhao, 1 andzhenganyao 1 department of mathematics and computational science, sun yatsen university, guangzhou, china school of mathematics and information science, shaoguan university, shaoguan, china. For the hyperchaotic lorenz 4d system the extra parameter. 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. Diffusive synchronization of hyperchaotic lorenz systems. Hyperchaos and hyperchaos control of the sinusoidally. Complexity analysis and dsp implementation of the fractional. Secondly, the dynamical behaviors of the proposed system, such as the dissipative property and equilibrium point, are discussed. In consideration of the advantages of the fractionalorder system and the hyperchaotic system, this paper addresses a new image encryption algorithm based on the fractionalorder hyperchaotic lorenz system. In order to solve the chaos synchronization problem for a hyperchaotic lorenz type system, we propose an observer based synchronization under a masterslave configuration. By modifying a generalized lorenz system, a new 5d hyperchaotic system was presented by yang and bai 26. Global chaos synchronization of hyperchaotic lorenz and. In 12, hyperchaotic behavior of an integerorder nonlinear system with unstable oscillators. Maps may be parameterized by a discretetime or a continuoustime parameter.
The lorenz attractor, a paradigm for chaos 3 precision. A new hyperchaos system and its circuit simulation by ewb. A new 5d hyperchaotic system based on modified generalized. Yet, the theory would be rather poor if it was limited to this absence of determinism and did not encompass any deductive aspect. Reference 6 has reported a hyperchaotic system based on. Global chaos synchronization of hyperchaotic lorenz and hyperchaotic chen systems by adaptive control dr.
Synchronization of an uncertain new hyperchaotic lorenz system is studied in this paper. A sinusoidally driven lorenz system and circuit implementation. In 1963, lorenz discovered the famous lorenz chaotic system 1. Lorenz system in order to show how backstepping design works, in this section the tool is applied for controlling the chaotic dynamics of the lorenz system. Lassoued and boubaker have done a literature survey on new chaotic and hyperchaotic systems 15. After the discovery of lorenz chaotic system 1, chaos theory, chaosbased applications, and new chaotic systems have been studied intensively 2. Pdf complexity analysis and dsp implementation of the. The hyperchaotic lorenz system is studied by bifurcation diagram, lyapunov exponents spectrum and phase diagram. Chaos synchronization for hyperchaotic lorenztype system via. Projective synchronization for a class of 6d hyperchaotic lorenz system article pdf available in telkomnika indonesian journal of electrical engineering 162. Dynamics of a hyperchaotic lorenz system international. A new image encryption algorithm based on the fractional.
Request pdf a hyperchaos generated from lorenz system this paper presents a fourdimension hyperchaotic lorenz system, obtained by adding a nonlinear controller to lorenz chaotic system. In this paper, synchronization of fourdimensional hyperchaotic lorenz system, drive system with the chens system response system are investigated based on backstepping technique. Karthikeyan research scholar, school of electronics and electrical engineering. This intentionally constructed 4d chaotic system doesnt reincarnate known hyperchaotic patterns. Systems description in this work, two nonlinear systems are studied, namely, chaotic lorenz system and hyperchaotic lorenz system.
Dynamic analysis of a 5d fractionalorder hyperchaotic system. Another approach is developed for generating twowing hyperchaotic attractor, fourwing chaotic attractor, and high periodic orbits such as period14 from a sinusoidally driven based canonical lorenz system. A hyperchaos generated from lorenz system sciencedirect. Unlike the wellknown i j, multiswitching of the indices was employed in the usual masterslave synchronization scheme. Mahmoud 1 aug 2010 mathematics and computers in simulation, vol. The following 4d hyperchaotic system of lorenz type was presented in where state variables of the system are denoted by, and, the parameters of the system are represented by, and, and the dot above state variables refers to time derivative of state variables. Combined with one null exponent along the flow and one negative exponent to ensure the boundness of the solution, the minimal dimension for a continuous hyperchaotic system is 4. Lorenz system, hyperchaotic, projective synchronization 1 introduction chaos is a very interesting nonlinear phenomenon. Zerohopf bifurcation in a hyperchaotic lorenz system. Bifurcations of fractionalorder diffusionless lorenz. A new fourdimensional continuoustime autonomous hyperchaotic lorenztype system is introduced and analyzed. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. Synchronization of hyperchaotic lorenz system based. In figure 1, the two largest tle for singlevariable coupling are plotted as a function of k,forr 30.
Sundarapandian professor, research and development centre vel tech dr. The system is hyperchaotic in a wide range of parameters. On the contrary, i want to insist on the fact that, by asking the good questions, the theory is able to. Projective synchronization of a hyperchaotic lorenz system. Fuzzy adaptive synchronization of timereversed chaotic. Pdf a hyperchaotic system without equilibrium yanxia sun. The state orbits of the hyperchaotic lorenz system 1 are shown in fig. Gps of nonidentical hyperchaotic lorenz and hyperchaotic qi systems via adaptive control, when the system parameters are unknown.
Synchronization and control of hyperchaotic complex lorenz system gamal m. Dq t0 is the caputo fractional derivative with the order 0 hyperchaotic lorenz type system. Le 1 le 2 0, le 3 0, le 4 hyperchaotic system into the 3d phase portraits. A symmetric controllable hyperchaotic hidden attractor mdpi. This paper reports a new fivedimensional 5d hyperchaotic system with three positive lyapunov exponents, which is generated by adding a linear controller to the second equation of a 4d system that is obtained by coupling of a 1d linear system and a 3d modified generalized lorenz system. Hyperchaos and hyperchaos control of the sinusoidally forced simpli. Multiswitching synchronization of nonidentical hyperchaotic. The hyperchaotic lorenz system is one of the paradigms of the fourdimensional hyperchaotic systems discovered by g. Complexity of this system versus parameters are analyzed by lces, bifurcation diagrams, phase portraits, complexity algorithms. Synchronization and control of hyperchaotic complex lorenz system. Hybrid adaptive synchronization of hyperchaotic systems with. Pdf it is often difficult to obtain the bounds of the hyperchaotic systems due to very complex algebraic structure of the hyperchaotic systems.
1363 241 1116 1057 1283 739 15 343 1290 45 1357 1653 689 366 1356 788 215 94 859 588 531 1187 364 585 611 1633 461 1212 1006 250 1004 1168 1416 312 488 323 1293 1192 821