Hyperchaotic systems have applications in multiple areas of science and engineering. Global chaos synchronization of hyperchaotic lorenz and. 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. Systems description in this work, two nonlinear systems are studied, namely, chaotic lorenz system and hyperchaotic lorenz system. In this paper, synchronization of fourdimensional hyperchaotic lorenz system, drive system with the chens system response system are investigated based on backstepping technique.
This hyperchaotic system is not only visualized by computer simulation but also verified with bifurcation analysis and realized with an electronic circuit. Dynamics of a hyperchaotic lorenz system international. Secondly, the dynamical behaviors of the proposed system, such as the dissipative property and equilibrium point, are discussed. A hyperchaos generated from lorenz system request pdf. Fractionalorder hyperchaotic lorenz system the fractionalorder hyperchaotic lorenz system is used in the encryption algorithm, which is described by 8. Le 1 le 2 0, le 3 0, le 4 hyperchaotic system into the 3d phase portraits. Bifurcations of fractionalorder diffusionless lorenz system. Generalized projective synchronization for different. Global chaos synchronization of hyperchaotic lorenz and hyperchaotic chen systems by adaptive control dr. Zerohopf bifurcation in a hyperchaotic lorenz system. 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. 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. A new hyperchaos system and its circuit simulation by ewb. The systems will never get synchronized if walone is the.
Lyapunov characteristic exponents lces of this system are calculated according to this deduced discrete map. The hyperchaotic lorenz system is one of the paradigms of the fourdimensional hyperchaotic systems discovered by g. Control and synchronization of a new hyperchaotic 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. Maps may be parameterized by a discretetime or a continuoustime parameter. A hyperchaos generated from lorenz system sciencedirect. Antisynchronization of the hyperchaotic lorenz systems by. In this section, the fractionalorder hyperchaotic lorenz system is presented, and a novel image encryption scheme is described in detail. After the discovery of lorenz chaotic system 1, chaos theory, chaosbased applications, and new chaotic systems have been studied intensively 2. Chaos synchronization for hyperchaotic lorenztype system via.
In mathematics, a chaotic map is a map evolution function that exhibits some sort of chaotic behavior. A 5d system with three positive lyapunov exponents was found by yang and chen 27. Pdf complexity analysis and dsp implementation of the. The lorenz attractor, a paradigm for chaos 3 precision. Multiswitching synchronization of nonidentical hyperchaotic. In 1963, lorenz discovered the famous lorenz chaotic system 1. International journal on computer science and engineering ijcse issn. 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. Complexity analysis and dsp implementation of the fractional.
Furthermore, based on lyapunov stability theory, an adaptive controller is designed and the new 4d hyperchaotic lorenz system is controlled at equilibrium point. Hybrid adaptive synchronization of hyperchaotic systems with. 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. Synchronization of an uncertain new hyperchaotic lorenz system is studied in this paper. Synchronization of hyperchaotic lorenz system based.
Research article control and synchronization of chaotic. A new fourdimensional continuoustime autonomous hyperchaotic lorenztype system is introduced and analyzed. Also, the approach may be suitable for practical implementationin some real systems. 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. By modifying a generalized lorenz system, a new 5d hyperchaotic system was presented by yang and bai 26. Complexity of this system versus parameters are analyzed by lces, bifurcation diagrams, phase portraits, complexity algorithms. Pdf on the dynamics of new 4d lorenztype chaos systems. For the hyperchaotic lorenz 4d system the extra parameter. Diffusive synchronization of hyperchaotic lorenz systems. 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 approximation is a coupling of the navierstokes equations with thermal convection.
A theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a. Hyperchaos and hyperchaos control of the sinusoidally forced simpli. Hyperchaotic attractor with multiple independent controllers. In 12, hyperchaotic behavior of an integerorder nonlinear system with unstable oscillators. Bifurcations of fractionalorder diffusionless lorenz. The generalized projective synchronization of hyperchaotic. Pdf memristorbased lorenz hyperchaotic system and its. A sinusoidally driven lorenz system and circuit implementation. This intentionally constructed 4d chaotic system doesnt reincarnate known hyperchaotic patterns.
Request pdf a hyperchaos generated from lorenz system this paper presents a fourdimension hyperchaotic lorenz system, obtained by adding a nonlinear. 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. The original problem was a 2d problem considering the thermal convection between two parallel horizontal plates. Dynamic analysis of a 5d fractionalorder hyperchaotic system. Dq t0 is the caputo fractional derivative with the order 0 hyperchaotic lorenz type system. Lorenz equations is preserved or removed, a new piecewise linear hyperchaotic system results with only signum and absolutevalue nonlinearities. Research article control and synchronization of chaotic and. The state orbits of the hyperchaotic lorenz system 1 are shown in fig. Coexisting hidden attractors in a 4d simplified lorenz system. First of all, a hyperchaotic system is constructed by introducing two state variables into the lorenz chaotic system.
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. 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. Numerical solution of the fractionalorder lorenz hyperchaotic system 2. Sundarapandian professor, research and development centre vel tech dr. Synchronization and control of hyperchaotic complex lorenz system.
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. Unlike the wellknown i j, multiswitching of the indices was employed in the usual masterslave synchronization scheme. Synchronization and control of hyperchaotic complex lorenz. A new image encryption algorithm based on the fractional. Numerical simulations show that the new systems behavior can be convergent, divergent, periodic, chaotic and hyperchaotic when the parameter varies.
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. 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. The lorenz system 1 formulation 1 formulation the lorenz system was initially derived from a oberbeckboussinesq approximation. Memristorbased lorenz hyperchaotic system and its circuit implementation ruan jingy a sun kehui mou jun. Based on the properties of a passive system, a passive controller is designed and the synchronization between two hyperchaotic lorenz systems under different. Chaos control and synchronization of a novel 5d hyperchaotic. Adaptive synchronization for an uncertain new hyperchaotic.
The hyperchaotic lorenz system is studied by bifurcation diagram, lyapunov exponents spectrum and phase diagram. Dynamical equations have seven terms without any quadratic or higher order polynomials and, to our knowledge, are the simplest hyperchaotic system. Pdf, application of hyperchaotic lorenz system for. 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. Fuzzy adaptive synchronization of timereversed chaotic. Since hyperchaotic system has the characteristics of high capacity, high security and high ef. Hyperchaos and hyperchaos control of the sinusoidally. Lorenz system of differential equations is used as a source for carriers of the chaotic spectrum.
Karthikeyan research scholar, school of electronics and electrical engineering. 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. A symmetric controllable hyperchaotic hidden attractor mdpi. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information.
Lorenz system, hyperchaotic, projective synchronization 1 introduction chaos is a very interesting nonlinear phenomenon. 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. The system is hyperchaotic in a wide range of parameters. Synchronization and control of hyperchaotic complex lorenz system gamal m. Mahmoud 1 aug 2010 mathematics and computers in simulation, vol. In this paper, we investigate the dynamics of the lorenz system, linearly extended into one additional dimension. Hyperchaos and hyperchaos control of the sinusoidally forced. Projective synchronization of a hyperchaotic lorenz system. When considering a fivedimensional selfexciting homopolar disc dynamo, wei et al. On the contrary, i want to insist on the fact that, by asking the good questions, the theory is able to.
In figure 1, the two largest tle for singlevariable coupling are plotted as a function of k,forr 30. After that, chaotic systems have been researched extensively, such as the lu system 24, the chen system 5 and the rossler system 6. Projective synchronization for a class of 6d hyperchaotic lorenz system article pdf available in telkomnika indonesian journal of electrical engineering 162. Research article a sinusoidally driven lorenz system and. Lassoued and boubaker have done a literature survey on new chaotic and hyperchaotic systems 15. The fractionalorder hyperchaotic lorenz system is solved as a discrete map by applying the adomian decomposition method adm. Reference 6 has reported a hyperchaotic system based on. Pdf a hyperchaotic system without equilibrium yanxia sun. A novel hyperchaotic system with fractionalorder terms has been proposed in 14.
437 1605 1426 801 528 280 265 5 1274 1041 716 1181 646 1132 1176 317 1095 1292 829 979 669 1314 842 843 1558 1319 21 1647 1319 799 164 996 1126 1300 412 1087 1262 5 175 367 1204 1179