We then investigate the estimation of the global attractive set and stochastic bifurcation behavior of the family of stochastic lorenz system. Dynamics and synchronization of the fractionalorder. Global chaos synchronization of hyperchaotic lorenz and. Besides, the most representative dynamics which may be found in this new system are located in the phase space and are analyzed here. A new ninedimensional chaotic lorenz system with quaternion. Reference 6 has reported a hyperchaotic system based on. Chaos control and synchronization of a novel 5d hyperchaotic. Homoclinic orbits and chaos in the generalized lorenz system. Adaptive synchronization for an uncertain new hyperchaotic. Controlling chaotic dynamics using backstepping design 1427 3. After that, chaotic systems have been researched extensively, such as the lu system 24, the chen system 5 and the rossler system 6. Dynamics and synchronization of new hyperchaotic complex. Coexisting hidden attractors in a 4d simplified lorenz system. Novel hyperchaotic system and its circuit implementation.
Furthermore, it is found that the hopf bifurcation occurs in this hyperchaotic system when the bifurcation parameter exceeds a critical value. The fractionalorder lorenz hyperchaotic system is solved as a discrete map by applying adomian decomposition method adm. Dynamics of a new 5d hyperchaotic system of lorenz type. This paper is devoted to the analysis of complex dynamics of a generalized lorenzstenflo hyperchaotic system. We study the influence of complex parameters on the dynamics and behaviors of nonlinear hyperchaotic models. A new fourdimensional, hyperchaotic dynamic system, based on lorenz dynamics, is presented. Taking the twodimensional grid sinusoidal cavity hyperchaotic map as an example, dynamics of the system are analyzed by phase diagram, equilibrium points, lyapunov exponents spectrum, bifurcation. A new 4d hyperchaotic system with a twoscroll attractor. 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. A new 5d hyperchaotic system based on modified generalized. Complicated dynamics and control of a hyperchaotic complex. It is very important to generate hyperchaos with more complicated dynamics as a model for theoretical research and practical application. Request pdf dynamics of a new 5d hyperchaotic system of lorenz type ultimate boundedness of chaotic dynamical systems is one of the fundamental concepts in dynamical systems, which plays an. 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.
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. As the slave system, we consider the controlled hyperchaotic lorenz dynamics described by. The lorenz attractor, a paradigm for chaos 3 precision. This paper introduces and analyzes new hyperchaotic complex lorenz systems. Dynamics of coupled lorenz systems and its geophysical. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers.
Generalized projective synchronization for different. Jul 26, 2018 by using a simple state feedback control technique and introducing two new nonlinear functions into a modified sprott b system, a novel fourdimensional 4d noequilibrium hyperchaotic system with grid multiwing hyperchaotic hidden attractors is proposed in this paper. Its jacobian matrix everywhere has rank less than 4. This paper discusses the complex dynamics of a new fourdimensional continuoustime autonomous hyperchaotic lorenztype system. In 12, hyperchaotic behavior of an integerorder nonlinear system with unstable oscillators. In section 3, dynamics and complexity of the system are analyzed and some interesting results are illustrated. Le 1 le 2 0, le 3 0, le 4 a paradigm for chaos 3 precision. We investigate the dynamics and synchronization of this new system. The new system is especially designed to improve the complexity of lorenz dynamics, which, despite being a paradigm to understand the chaotic dissipative flows, is a. The existence conditions of the homoclinic orbits are obtained by fishing principle. Dynamics of stochastic lorenz family of chaotic systems. Control and synchronization of a new hyperchaotic system. Pdf a hyperchaotic system without equilibrium yanxia.
Dynamics of coupled lorenz systems and its geophysical implications andrzej stefanski a, tomasz kapitaniak a. R 1 c a 3 where ris the rayleigh number and p10isthe prandtl number. Hopf equilibrium that is, an isolated equilibrium with double zero eigenvalues and a pair of purely imaginary eigenvalues of this hyperchaotic. Synchronization of an uncertain new hyperchaotic lorenz system is studied in this paper. First, on the local dynamics, the bifurcation of periodic solutions at the zero. A new five dimensional hyperchaotic system and its. We present the results of selfsynchronization by coupling two. The goal of this paper is to construct a new hyperchaotic complex lorenz system by adding a linear controller to 1 and to consider this new system as a generalization of the hyperchaotic real lorenz system 22. This paper discusses the complex dynamics of a new fourdimensional continuoustime autonomous hyperchaotic lorenz type system. Dynamics of a hyperchaotic lorenz system international.
A new hyperchaotic lorenzbased system inordertogetcomplexhyperchaos,wehaveconsideredthe. Hyperchaos and hyperchaos control of the sinusoidally forced. Using center manifold theory and lyapunov functions, we get nonexistence conditions of homoclinic orbits associated with the origin. Pdf a hyperchaotic system without equilibrium yanxia sun. Zerohopf bifurcation in a hyperchaotic lorenz system. Researcharticle improving the complexity of the lorenz. For example, even activepassivedecompositionschemes19,whereonlyone. A hyperchaotic attractor is typically defined as chaotic behavior with at least two positive lyapunov exponents. Based on the fractional derivative theory, the fractionalorder form of this new hyperchaotic system has been investigated. A 5d system with three positive lyapunov exponents was found by yang and chen 27. The hyperchaotic lorenz system is one of the paradigms of the fourdimensional hyperchaotic systems discovered by g. Antisynchronization of the hyperchaotic lorenz systems by. Numerical solution of the fractionalorder lorenz hyperchaotic system. Dynamics of a hyperchaotic map with spherical attractor.
As the master system, we consider the hyperchaotic lorenz dynamics described by 121 2124 312 3 423 xxx x x xxxx xxx x xrxx. A new hyperchaotic system with double piecewiselinear functions in state equations is presented and physically implemented by circuit design. A new 4d hyperchaotic system is constructed based on the lorenz system. Researcharticle improving the complexity of the lorenz dynamics. Yet, the theory would be rather poor if it was limited to this absence of determinism and did not encompass any deductive aspect. 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.
Gps of nonidentical hyperchaotic lorenz and hyperchaotic qi systems via adaptive control, when the system parameters are unknown. With three nonlinearities, this system has more than one positive lyapunov exponents. Hyperchaos and hyperchaos control of the sinusoidally. The lorenz equations the system considered herein is described by the following set of dynamic equations singer et al. The system is hyperchaotic in a wide range of parameters. A new simple fourdimensional equilibriumfree autonomous ode system is described. Dynamics of a hyperchaotic lorenztype system springerlink. The new system represents the continued transition from the lorenz to the chen system and is chaotic over the entire spectrum of the key system parameter.
Dynamics of a hyperchaotic lorenz system semantic scholar. Many hyperchaotic systemsbased onan extension of the famous lorenz 1963 system have been proposed li et al. It is a 3d autonomous system with six terms including only two. Complexity analysis and dsp implementation of the fractional. It is hyperchaotic in some regions of parameter space, while in other regions it has an attracting torus that coexists with either a symmetric pair of strange attractors or with. The goal of this paper is to construct a new hyperchaotic complex lorenz system by adding a linear controller to and to consider this new system as a generalization of the hyperchaotic real lorenz system. Since then, the hyperchaotic system has attracted more and more attention owning to its abundant and complex dynamic characteristics.
This paper investigates the homoclinic orbits and chaos in the generalized lorenz system. A novel fourdimensional noequilibrium hyperchaotic. Hyperchaos and hyperchaos control of the sinusoidally forced simpli. Ming chen, school of mathematics and systems science, guangdong polytechnic normal university, guangzhou 510665, china.
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. 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. In this paper, we investigate the dynamics of the lorenz system, linearly extended into one additional dimension. Herein, we study its dynamics, basic properties, aas, and application to secure communication. Finally, an electronic circuit of the new hyperchaotic system with multisim is designed and a good match between the plots of the theoretical model and the circuit model of the new hyperchaotic system is shown. By using a simple state feedback control technique and introducing two new nonlinear functions into a modified sprott b system, a novel fourdimensional 4d noequilibrium hyperchaotic system with grid multiwing hyperchaotic hidden attractors is proposed in this paper. It shows the attractor of hyperchaotic lorenz dynamical system at a 10,r 28,b 83, and d 1. 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. On the dynamics in parameter planes of the lorenzstenflo system. Results show that this system has rich dynamical behaviors. Request pdf dynamics and synchronization of new hyperchaotic complex lorenz system a b s t r a c t the aim of this paper is to introduce a new hyperchaotic complex lorenz system.
The complex parameters such as generalized hamiltonian, symmetry, dispersal, equilibria and their stability, lyapunov exponents, lyapunov. Equivalent 3d subsystem is obtained by comparing the movements of the trajectories of the original hyperchaotic systems with all of their 3d subsystems. When considering a fivedimensional selfexciting homopolar disc dynamo, wei et al. In 1963, lorenz discovered the famous lorenz chaotic system 1. Lorenz system, hyperchaotic, projective synchronization 1 introduction chaos is a very interesting nonlinear phenomenon. In section 4, the system is implemented by dsp, then a pseudorandom bit generator is designed based on the implemented system. Oct 21, 2011 a hyperchaotic attractor is typically defined as chaotic behavior with at least two positive lyapunov exponents.
Thus, system is a 7dimensional 7d continuous real autonomous hyperchaotic system, while most of hyperchaotic systems in the literature are 4d systems. 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. A new hyperchaos system and its circuit simulation by ewb. On the dynamics of a highorder lorenz stenflo system paulo c rechspiral organization of periodic structures in the lorenz stenflo system paulo c rechcharacterization of hyperchaotic states in the parameterspace of a modified lorenz system marcos j correia and paulo c rechrecent citations spiral organization of periodic structures in. By modifying a generalized lorenz system, a new 5d hyperchaotic system was presented by yang and bai 26. On the contrary, i want to insist on the fact that, by asking the good questions, the theory is able to.
It shows the attractor of hyperchaotic lorenz dynamical system at a 10,r 28,b 83, and. Dynamics of a hyperchaotic lorenz system request pdf. Le 1 le 2 0, le 3 0, le 4 system with an order as low as 2. The system has seven terms, two quadratic nonlinearities, and only two parameters.
This new model is a ninedimensional 9d system of real. 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. In this paper, a new fivedimensional hyperchaotic system by introducing two additional states feedback into a threedimensional smooth chaotic system. Control and synchronization of hyperchaotic states in. A novel fourdimensional noequilibrium hyperchaotic system. However, these lorenzlike systems have more than seven terms and more than two parameters, and thus it is di. Extensive and indepth researches have been carried out, such as the modified hyperchaotic system, circuit implementation of hyperchaotic systems 24, especially in synchronous. The hyperchaotic qi system chen, yang, qi and yuan, 2007 is described by the 4d dynamics. Projective synchronization of a hyperchaotic lorenz system. 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.