Search

Electromagnetic induction plays a key role in regulating the electrical activity, excitability, and bistable structure of neurons. In this paper, a discontinuous control strategy with membrane potential as the threshold is introduced to the HR neuron model under the influence of electromagnetic field (EMFN model), and then we establish a Filipov EMFN neuron model to realize the regulation effect of electromagnetic field on the neuron system. Specific work of this paper reads as follows: first, the existence and stability of equilibrium points of two subsystems are analyzed by using MatCont software; second, the bistable region and its internal mechanism are discussed in detail by two-parameter bifurcation analysis; third, the mechanism of bistability and a series of complex sliding mode dynamics including sliding segment and sliding bifurcations are further revealed with the help of the fast–slow variable dissection method; finally, based on Hamilton energy, the regulation of threshold on chaotic discharge in the Filippov EMFN neuron model is explored. The numerical simulation results show that the EMFN neuron model can produce the corresponding sliding limit cycle and sliding bursting behaviors under the influence of the threshold control strategy, meanwhile, the chaotic behavior of the new system can be controlled effectively within a certain range. The results provide ideas for controlling the effects of electromagnetic fields on the biological neuronal system and exploring the regulation mechanism of neurological diseases. [ABSTRACT FROM AUTHOR]

This paper puts forward a novel image encryption algorithm that is based on permutation-diffusion architecture. In pixels' permutation stage, algorithm takes full advantage of the idea of magic cube's scrambling. There is only simple cyclic shift operation in each sub-block's permutation, but when the algorithm has disposed the current sub-block, the adjacent sub-blocks will be dealt with, too. In the cyclic shift of each row, stable points will help to decrease the correlation of adjacent pixels. To make encryption procedure uncertain, this paper brings in a parameter named delay-time that is generated by chaotic map. In the diffusion stage, by combining multiple operations and dynamic look-up table together, the proposed algorithm highly increases the uncertainty of the encryption procedure. At last, the experiment results of key space analysis, information entropy analysis, histogram analysis and etc. show that the encryption algorithm has well performance and it can be used in image encryption and transmission. [ABSTRACT FROM AUTHOR]

This paper presents a four-dimensional hyperchaos Qi system, obtained by adding linear term and nonlinear term of nonlinear controller to Qi chaos system. The hyperchaos Qi system is studied by bifurcation diagram, Lyapunov exponent spectrum and phase diagram. Numerical simulations show that the new system's behavior can be periodic, chaotic and hyperchaotic as the parameter varies. [ABSTRACT FROM AUTHOR]

In this paper, we propose a dynamic delayed feedback control approach or desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two different populations of globally coupled chaotic-bursting neurons. The proposed method has potential for mild, effective and demand-controlled therapy of neurological diseases characterized by pathological synchronization. [ABSTRACT FROM AUTHOR]

This paper offers two different attacks on a freshly proposed image encryption based on chaotic logistic map. The cryptosystem under study first uses a secret key of 80-bit and employed two chaotic logistic maps. We derived the initial conditions of the logistic maps from using the secret key by providing different weights to all its bits. Additionally, in this paper eight different types of procedures are used to encrypt the pixels of an image in the proposed encryption process of which one of them will be used for a certain pixel which is determined by the product of the logistic map. The secret key is revised after encrypting each block which consisted of 16 pixels of the image. The encrypting process have weakness, worst of which is that every byte of plaintext is independent when substituted, so the cipher text of the byte will not change even the other bytes have changed. As a result of weakness, a chosen plaintext attack and a chosen cipher text attack can be completed without any knowledge of the key value to recuperate the ciphered image. [ABSTRACT FROM AUTHOR]

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper proposes a new symmetric key encryption algorithm based on one-dimensional chaotic map. This algorithm uses the random-like property and ergodicity of chaotic systems. In the process of encryption or decryption, this algorithm generates a chaotic pseudo-random sequence, changes the initial iterative times and the increment to encrypt the plaintext, and realizes fast encryption and decryption of all kinds of files. When analyzing the algorithm's performance and security, the result shows that, compared with the method of Baptista, the proposed method is safer, faster and more powerful. [ABSTRACT FROM AUTHOR]

In this paper, lag full state hybrid projective synchronization (LFSHPS) in fractional-order chaotic systems is first studied. We show that LFSHPS does exist in fractional-order chaotic systems. Based on active control theory, synchronization schemes for LFSHPS of the fractional-order chaotic systems are given. Numerical simulations are provided to illustrate and verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper studies chaos synchronization via unidirectional coupling. The self-synchronization of Lorenz systems, modified coupled dynamos systems and hyperchaotic Chen systems is studied by three methods: the Lyapunov function method, the global synchronization method and the numerical calculation of the largest Lyapunov exponent method. In regard to application to communication, we show that via transmitting single signal the synchronization of the drive system and the response system can be achieved. An example of applying self-synchronization of hyperchaotic Chen systems to chaotic masking secure communication is presented in this paper. Simulation results show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, the chaotic phenomenon is reported in a bearing system. The chaotic dynamics of the new system is first derived from an available bearing system. The proposed system is then analyzed using various tools to observe its dynamical behaviors. Theoretical and simulation results confirm the presence of chaotic and periodic behaviors in the new bearing system. [ABSTRACT FROM AUTHOR]

In this paper, the quantum system with two particles is analyzed and the energy level spacing statistics distribution and Δ3-statistic are given. The results show that hard quantum chaos appear in the system with a certain potential. Tunnelling effect develops quantum chaos. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds back the development of chaos. [ABSTRACT FROM AUTHOR]

In this paper, we present a selective image encryption system based on couple spatial chaotic systems, the cascade one-dimensional Logistic map and high-dimensional spatial chaotic system has been used to generate the adequate encryption sequence, then the selective gray-level image encryption is implemented with the sequence, which can greatly improve the encryption performance and efficiency. In addition, we also adopt an index array to control the generation of the secret key, a completely different cipher text will be obtained if a pixel's value is altered in the original image, which can resist the differential attack effectively. [ABSTRACT FROM AUTHOR]

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Aiming at the drawbacks of the chaotic masking scheme, this paper optimizes this conventional scheme by using improved state observer method and system-alternating method, proposes a new secure communication scheme which can improve these drawbacks of chaotic method: (1) Restriction that the power of useful signal must be smaller than that of chaotic signal. (2) Low security. In addition, the model of this whole communication system is constructed under the system simulation environment of Simulink. [ABSTRACT FROM AUTHOR]

This paper presents the general method for the adaptive function Q-S synchronization of different chaotic (hyper-chaotic) systems. Based upon the Lyapunov stability theory, the dynamical evolution can be achieved by the Q-S synchronization with a desired scaling function between the different chaotic (hyper-chaotic) systems. This approach is successfully applied to two examples: Chen hyper-chaotic system drives the Lorenz hyper-chaotic system; Lorenz system drives Lü hyper-chaotic system. Numerical simulations are used to validate and demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

An epidemic spreading through an adaptive network, where the susceptible are able to avoid contact with the infective by rewiring their network connections, with random and regular contacts is considered. This paper uses a new mathematical model obtained by pair approximation to explore the effect of rewiring of the epidemic dynamics. We show that chaotic behavior can emerge while considering rewiring. The obtained results show that rewiring plays an very important role on the dynamical behavior of the epidemic model. [ABSTRACT FROM AUTHOR]

This paper studies the problem of chaos synchronization between two different hyperchaotic systems with uncertain parameters. Based on the Lyapunov stability theory, we obtain the sufficient condition of synchronization between two different hyperchaotic systems with uncertain parameters. A new adaptive controller with parameter update laws is designed to synchronize these chaotic systems. We proved it in theory with an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Rössler system. Numerical results verified the validation of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor-corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time chaos synchronization of a new hyperchaotic Lorenz system. Based on the finite-time stability theory, a simple and robust controller is proposed to realize finite-time chaos synchronization for the hyperchaotic Lorenz system. Theoretical analysis proved that the scheme can ensure the error system globally finite-time stable. Numerical simulations are provided to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper investigates the global synchronization problem of master-slave coupled multi-scroll saturated chaotic systems via single-state linear feedback control. An algebraic criterion for global synchronization is rigorously proven by means of the absolute stability theory. The obtained algebraic criterion is then optimized thereby deriving a less-conservative result, which is finally verified by numerical examples. [ABSTRACT FROM AUTHOR]

In order to solve the problem of degradation of dynamical properties caused by finite states of computer, a new binary stream-cipher algorithm based on dual one-dimensional chaotic maps is proposed in this paper. In the process of generation, we employ a parameter of one chaotic map to perturb the other chaotic map's trajectory to lengthen the cycle-length of the other chaotic map's trajectory. In addition, we design a nonlinear principle to generate a pseudo-random chaotic bit sequence as key stream. Statistic proprieties show that the sequence is of high randomness. [ABSTRACT FROM AUTHOR]

Such a problem, how to resolve the problem of long-term unpredictability of chaotic systems, has puzzled researchers in nonlinear research fields for a long time during the last decades. Recently, Voss et al. had proposed a new scheme to research the anticipating synchronization of integral-order nonlinear systems for arbitrary initial values and anticipation time. Can this anticipating synchronization be achieved with hyper-chaotic systems? In this paper, we discussed the application of anticipating synchronization in hyper-chaotic systems. Setting integer order and commensurate fractional order hyper-chaotic Chen systems as our research objects, we carry out the research on anticipating synchronization of above two systems based on analyzing the stability of the error system with the Krasovskill-Lyapunov stability theory. Simulation experiments show anticipating synchronization can be achieved in both integer order and fractional order hyper-chaotic Chen system for arbitrary initial value and arbitrary anticipation time. [ABSTRACT FROM AUTHOR]

This paper studies the generalized synchronization of hyperchaos systems, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. This new method has more extensive application scope. Based on the Lyapunov stability theory, the correctness of the proposed scheme is strictly demonstrated. It is also illustrated by applications to hyperchaotic Chen system and hyperchaotic Lorenz system and the simulation results show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studies full state hybrid projective synchronization of the unified chaotic system with unknown parameters. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with unknown parameters asymptotically full state hybrid projective synchronized. Numerical simulations show the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a new block encryption algorithm. The chaotic trajectories are computed by weighting. Then the result is used to mask the plaintext. Multiple blocks of plaintext are encrypted at the same time and this decreases the chaotic iterations. So the encryption speed is improved to some extent. The proposed algorithm is flexible. When the number of weights is increased, the number of the encrypted plaintext block at the same time is increased and the encryption speed is improved. The simulation result shows that the proposed algorithm has fast encryption speed and fine security. [ABSTRACT FROM AUTHOR]

In this paper, periodic parametric perturbations are used to control chaos in Liu system. By changing the frequency of the perturbation signal, Liu system can be guided to not only periodic motion but also hyperchaos. Phase diagram, bifurcation diagram, Lyapunov exponents spectrum and Poincáre map are used to analyze the dynamic behavior of the controlled system in the numerical simulations, which show the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new $\mathcal{H}_{\infty}$ lag synchronization scheme for a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, the $\mathcal{H}_{\infty}$ lag synchronization controller is presented to not only guarantee exponential lag synchronization but also reduce the effect of external disturbance to an $\mathcal{H}_{\infty}$ norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. As an application of the proposed method, the $\mathcal{H}_{\infty}$ lag synchronization problem for Genesio-Tesi system is investigated. [ABSTRACT FROM AUTHOR]

The Šil'nikov homoclinic theorem provides one analytic criterion for proving the existence of chaos in three-dimensional autonomous nonlinear systems. In applications of the theorem, however, the existence of a homoclinic orbit that usually determines the geometric structure of the chaotic attractor is not easily verified mainly because there are no available efficient methods. In this paper, based on the undetermined coefficient approach we present a framework of how to find homoclinic orbits in two classes of three-dimensional autonomous nonlinear systems of normal forms, including how to set a reasonable form of expanding series of the homoclinic orbit, how to determine all coefficients in the expansion, and how to find a numerical homoclinic orbit. Numerical examples show that the proposed framework in combination with computer simulation is very efficient. [ABSTRACT FROM AUTHOR]

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

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. 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. The new findings are not only demonstrated by computer simulations but also verified with bifurcation analysis, Lyapunov exponents and Lyapunov dimension. [ABSTRACT FROM AUTHOR]

This paper investigates properties of synchronization of trigonometric coupled maps. These maps have some advantages, such as an invariant measure, ergodicity and the possibility of Kolmogorov-Sinai (KS) entropy calculation. Moreover, an encryption algorithm based on a synchronized coupled map is suggested and described in detail. Also, some security analyses are presented to illustrate the effectiveness of the proposed scheme. The cryptosystem's speed is analyzed as well. Results of the various types of analysis are encouraging and it can be concluded that the proposed image encryption technique is a suitable choice for practical applications. [ABSTRACT FROM AUTHOR]

This paper deals with a new fractional calculus based method to stabilize fixed points of single-input 3D systems. In the proposed method, the control signal is determined by fractional order integration of a linear combination of the system linearized model states. The tuning rule for this method is based on the stability theorems in the incommensurate fractional order systems. The introduced technique can be used in suppression of chaotic oscillations. To evaluate the performance of the proposed technique in practical applications, it has been experimentally applied to control chaos in two chaotic circuits. [ABSTRACT FROM AUTHOR]

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, we tune the linear coupling parameter to obtain the two Rössler oscillators in a synchronized regime and analyze the effect of a nonlinear coupling on the phase synchronized state. It demonstrates that the detuning parameter σ between the two natural frequencies ω1 and ω2 affects phase dynamics, and with the increase of the nonlinear coupling strength, for the primary resonance, the effect of phase synchronization between two sub-systems was decayed, while increasing with frequency ratio 1:2. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the nonlinear coupling strength. [ABSTRACT FROM AUTHOR]

This paper analyzes the security of a recent cryptosystem based on the ergodicity property of chaotic maps. It is shown how to obtain the secret key using a chosen-ciphertext attack. Some other design weaknesses are also shown. [ABSTRACT FROM AUTHOR]

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a tracking control strategy for a class of chaotic systems. A general tracking controller is designed. It is proved theoretically that the error signal can exponentially converge to zero. Numerical simulations show that the controller can make the output signal track all kinds of reference signals. Besides, a better effect can be obtained via changing the control parameters properly. [ABSTRACT FROM AUTHOR]

Let (∑, ρ) be a one-sided symbolic space (with two symbols) and σ be the shift on ∑. Denote the set of almost periodic points by A(·) and the set of weakly almost periodic points by W(·). In this paper, we prove that there exists an uncountable set J such that σ|J is distributively chaotic in a sequence, and J⊂W(σ)-A(σ). [ABSTRACT FROM AUTHOR]

Chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the phase and lag synchronization in coupled two fractional order chaotic oscillators. It is shown that with the increase of coupling strength, the system first undergoes a transition to phase synchronization, and when the coupling strength is increased further, another transition to lag synchronization occurs. It is further shown that the system with two chaotic oscillators of different orders can also exhibit phase synchronization phenomena, although the identical synchronization is impossible in this case. [ABSTRACT FROM AUTHOR]

The paper analyses the limitation of Baptista cryptography in partitioning an attractor, and proposes two new attractor-partition methods: uniform-partition algorithm and dynamic-partition algorithm. They are different from the equal-interval-partition algorithm in Baptista cryptography, but dividing the attractor according to the attractor's natural invariant density and plaintext density, respectively. The comparative experiment indicates: the two new methods improve the unbalanced cryptograph distribution and cryptograph length in Baptista cryptography, they are also able to reduce the iteration time in chaotic systems effectively, which has improved decryption time and cryptographies' security. [ABSTRACT FROM AUTHOR]

In this paper, we consider a continuous map f: X→X, where X is a compact metric space, and discuss the existence of a chaotic set of f specially (as X=[0,1]). We prove that f has a positively topological entropy if and only if it has an uncountably chaotic set in which each point is recurrent and is not weakly periodic. [ABSTRACT FROM AUTHOR]

In this paper, we numerically investigate the chaotic behaviors of the fractional-order Chua's circuit with a piecewise-linear nonlinearity. We find that chaos exists in the fractional-order Chua's circuit with order less than 3. The lowest order we find to have chaos is 2.7 in the homogeneous fractional-order Chua's circuit and 2.8 in the unhomogeneous fractional-order Chua's circuit. Our results are validated by the existence of a positive Lyapunov exponent. A chaos synchronization method is also presented for synchronizing the homogeneous fractional-order chaotic Chua's systems. The approach, based on stability theory of fractional-order linear systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method. [ABSTRACT FROM AUTHOR]

In this paper, a new model of evolving networks is proposed based on the dynamical behaviors of nodes in the network. The probability that an existing node in the current network receives a new link from the newly added node is proportional to the defined "activity" of that particular node, which is equivalent to the energy signal of the system from a control theory point of view. This network is found to have the scale-free feature with the degree distribution in a power-law form. This model provides another explanation for the emergence of scale-free networks in many real-world examples. [ABSTRACT FROM AUTHOR]

In this paper, on the basis of the Laypunov stability and the cascade synchronization approach, an effectual scroll controller and improving cascade synchronization approach are derived. The chaotic attractor can be displayed to be lopsided, till to be 1-scroll and periodic via the different scroll controller. And the proposed synchronization technique is applied to the new system, which the synchronization controller obtained by improving cascade method and adaptive functions. Numerical results are used to verify the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

In recent years, a lot of chaotic cryptosystems have been proposed. However, most of these cryptosystems can encrypt only one plaintext in one encryption process. We call these cryptosystems single-plaintext-oriented cryptosystems. In this paper, the authors propose a new chaotic cryptosystem which can encrypt multiple plaintexts in one encryption process. The proposed cryptosystem is dedicated to encrypting multiple plaintexts in the situation of transmitting multiple secret files over public data communication network in one secure transmission. Experiments and theoretic analysis show that the proposed cryptosystem possesses high security and fast performance speed. They also show that the proposed cryptosystem is more secure than single-plaintext-oriented chaotic cryptosystems in this special situation. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, an image encryption algorithm based on couple multiple chaotic systems is presented. It made the one-dimensional Coupled Map Lattice (CML) formed by Skew Tent map as spatiotemporal chaotic system and made its output sequence as the initial value of logistic and meanwhile did iterative of specific times to get the final key sequence, and then did XOR operations with corresponding pixels to finish the encryption. Numerical analysis expresses that this algorithm has large enough space and high security. [ABSTRACT FROM AUTHOR]

Based on the stability theory of fractional order systems and the pole placement technique, this paper designs a synchronization scheme with the state observer method and achieves the projective synchronization of a class of fractional order chaotic systems. Taking an example for the fractional order unified system by using this observer controller, and numerical simulations of fractional order Lorenz-like system, fractional order Lü system and fractional order Chen system are provided to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other. [ABSTRACT FROM AUTHOR]