The dynamical behaviour of the erbium-doped fibre single-ring laser with an optical delay feedback is discussed. Simulation shows that as the delay rate increases, the lasing light displays period-doubling which leads...The dynamical behaviour of the erbium-doped fibre single-ring laser with an optical delay feedback is discussed. Simulation shows that as the delay rate increases, the lasing light displays period-doubling which leads to chaos and via reverse period-doubling route returns from chaos to periodic. At a particular delay rate the intermittently chaotic route to chaos is also observed. The identical synchronization based on chaos in this ring laser is demonstrated by numerical simulation.展开更多
Chaotic communication is a rather new and active field of research. Althoughit is expected to have promising advantages, some investigators provide evidences that chaoticcommunication is not safety. This letter provid...Chaotic communication is a rather new and active field of research. Althoughit is expected to have promising advantages, some investigators provide evidences that chaoticcommunication is not safety. This letter provides a new chaotic secure communication scheme based ona generalized synchronization theory of coupled system. The secret message hidden in the chaoticsource signal generated via the scheme is very difficult to be unmasked by so-called nonlineardynamic forecasting technique. One example for Internet communications was presented to illustratethe security of our scheme.展开更多
Using an example, it was analytically proved that the dynamical systems constructed on a star coupled network is more easy to be synchronized than that in coupled map lattices (CML). The result shows that the synchron...Using an example, it was analytically proved that the dynamical systems constructed on a star coupled network is more easy to be synchronized than that in coupled map lattices (CML). The result shows that the synchronization in small-world networks may be realized more easily. Key words Lyapunov exponent - chaotic synchronization - small-world networks MSC 2000 37D45 Project supported by the National Natural Science Foundation of China(Grant No. 10171061)展开更多
A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple ...A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively. This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.展开更多
A new kind of secure communication system which combines the chaotic encryption means with the conventional encryption method is discussed. With the analysis results and the experiment data, the anti-attack ability of...A new kind of secure communication system which combines the chaotic encryption means with the conventional encryption method is discussed. With the analysis results and the experiment data, the anti-attack ability of this communication system is significantly improved compared to that of the either method. At the same time, a new method of chaotic synchronization is proposed. With a small mixed discrete chaotic signal, it is quickly to synchronize the communication and a good security performance is ensured.展开更多
This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochast...This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.展开更多
This paper detects and characterizes the diverse roles played by bounded noise in chaotic phase synchronization (CPS) of weakly coupled nonlinear stochastic systems. Analysis of a paradigmatic model of two bidirecti...This paper detects and characterizes the diverse roles played by bounded noise in chaotic phase synchronization (CPS) of weakly coupled nonlinear stochastic systems. Analysis of a paradigmatic model of two bidirectional coupled three-level food chains is carried out by various statistical measures such as Shannon entropy and mutual information. The results indicate that inside the synchronous regime, CPS is considerably reduced under the influence of bounded noise; near the onset of phase synchronization, temporal phase locking is diversely changed with the increase of noise, i.e., either weak or strong noise also degrades the degree of CPS, while intermediate noise enhances CPS remarkably, and an optimal noise intensity is detected that maximizes the enhancement.展开更多
A new synchronization scheme for chaotic(hyperchaotic) maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach ...A new synchronization scheme for chaotic(hyperchaotic) maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features:(i) it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;(ii) it is rigorous,being based on theorems;(iii) it can be readily applied to any chaotic(hyperchaotic) maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map(as the drive system) and the three-dimensional hyperchaotic Wang map(as the response system),and the three-dimensional H′enon-like map(as the drive system) and the two-dimensional Lorenz discrete-time system(as the response system).展开更多
This paper numerically investigates the effects of dispersion on optical fibre chaotic communication, and proposes a dispersion compensation scheme to improve the performance of optical fibre chaotic communication sys...This paper numerically investigates the effects of dispersion on optical fibre chaotic communication, and proposes a dispersion compensation scheme to improve the performance of optical fibre chaotic communication system. The obtained results show that the transmitter-receiver synchronization progressively degrades and the signal-to-noise ratio of the recovered message deteriorates as the fibre length increases due to the dispersion accumulation. Two segments of 2.5-km dispersion-compensating fibres are symmetrically placed at both ends of a segment of 245-km nonzero dispersionshifted fibre with low dispersion in one compensation period. The numerical results show that the signal-to-noise ratio of the extracted 1 GHz sinusoidal message is improved from -2.92 dB to 15.38 dB by this dispersion compensation for the transmission distance of 500 km.展开更多
The theories of synchronization based on secure communications using digital chaos are presented. A new synchronous method-cycles-interval Pulse drive is developed and realized. Experimental results show it is availab...The theories of synchronization based on secure communications using digital chaos are presented. A new synchronous method-cycles-interval Pulse drive is developed and realized. Experimental results show it is available, and in order to reduce synchronous noise, a method using model references solves the ratio of signal power to noise power, so the secure communication system can be realized.展开更多
The adaptive coupled synchronization method for non-autonomous systems is proposed. This method can avoid estimating the value of coupling coefficient. Under the uniform Lipschitz assumption, we derive the asymptotica...The adaptive coupled synchronization method for non-autonomous systems is proposed. This method can avoid estimating the value of coupling coefficient. Under the uniform Lipschitz assumption, we derive the asymptotical synchronization for a general coupling ring network with N identical non-autonomous systems~ even when N is large enough. Strict theoretical proofs are given. Numerical simulations illustrate the effectiveness of the present method.展开更多
We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-...We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-adaptive mechanism correctly represents essential characteristics of self-adaptation in complex systems. We also show that this method is reasonable both from the coupling viewpoint in physics and from the controller design viewpoint in control theory.展开更多
The digital communication of two-dimensional messages is investigated when two solid state multi-mode chaotic lasers are employed in a master-slave configuration. By introducing the time derivative of intensity differ...The digital communication of two-dimensional messages is investigated when two solid state multi-mode chaotic lasers are employed in a master-slave configuration. By introducing the time derivative of intensity difference between the receiver (carrier) and the transmittal (carrier plus signal), several signals can be encoded into a single pulse. If one signal contains several binary bits, two-dimensional messages in the form of a matrix can be encoded and transmitted on a single pulse. With these improvements in secure communications using chaotic multi-mode lasers, not only the transmission rate can be increased but also the privacy can be enhanced greatly.展开更多
A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic synchronization (LSISAAS) method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are consider...A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic synchronization (LSISAAS) method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are considered as system states. The LSISASS strategy depends on the only information, i.e. one state of the master system. According to the LSIST, the LSISASS method can asymptotically synchronize fully the states of the master system and the unknown system parameters as well. Simulation results also validate that the LSISAAS approach can obtain asymptotic synchronization.展开更多
A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable ...A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its (q-order and 2q-order) time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its (q-order and 2q-order) time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.展开更多
To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors (CMPS) of real chaotic systems and complex chaotic systems, where...To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors (CMPS) of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.展开更多
The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively.However,the coupled oscillators in practice are nonidentical,and there exist mismatched param...The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively.However,the coupled oscillators in practice are nonidentical,and there exist mismatched parameters.It has been proved that under certain conditions,complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points,yet other cooperative behaviors are not addressed.In this paper,we further consider two coupled nonidentical oscillators with the same equilibrium points,where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors.We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings.In the case of directed coupling,death islands appear in two-parameter spaces.The mechanism inducing these transitions is presented.展开更多
This paper has designed 2-channel dense wavelength division multiplexing (DWDM) chaotic sys- tem at the frequencies of 193.1 and 193,2THz, respec- tively. The optical chaotic signals were produced by using the semic...This paper has designed 2-channel dense wavelength division multiplexing (DWDM) chaotic sys- tem at the frequencies of 193.1 and 193,2THz, respec- tively. The optical chaotic signals were produced by using the semiconductor laser that is numerically modeled by employing laser rate equations. These two channels were multiplexed and then propagated through single mode optical fiber (SMF) of 80kin length with dispersion compensating fiber of 16 km length. Erbium doped fiber amplifier (EDFA) was used to compensate the power losses in the SMF. In lhis paper, we investigated the effects of polarization mode dispersion (PMD) and nonlinearities especially stimulated Raman scattering (SRS) on 2 channel DWDM chaotic communication system by varying the length of the SMF and value of differential group delay (DGD).展开更多
Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of couple...Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 60372061).
文摘The dynamical behaviour of the erbium-doped fibre single-ring laser with an optical delay feedback is discussed. Simulation shows that as the delay rate increases, the lasing light displays period-doubling which leads to chaos and via reverse period-doubling route returns from chaos to periodic. At a particular delay rate the intermittently chaotic route to chaos is also observed. The identical synchronization based on chaos in this ring laser is demonstrated by numerical simulation.
基金This project is jointly supported by the National Natural Science Foundation of China (No.60074034, 70271068), the Research Fund for the Doctoral Program of Higher Education (N0.200200080004) and the Foundation for University Key Teacher by the Ministry
文摘Chaotic communication is a rather new and active field of research. Althoughit is expected to have promising advantages, some investigators provide evidences that chaoticcommunication is not safety. This letter provides a new chaotic secure communication scheme based ona generalized synchronization theory of coupled system. The secret message hidden in the chaoticsource signal generated via the scheme is very difficult to be unmasked by so-called nonlineardynamic forecasting technique. One example for Internet communications was presented to illustratethe security of our scheme.
文摘Using an example, it was analytically proved that the dynamical systems constructed on a star coupled network is more easy to be synchronized than that in coupled map lattices (CML). The result shows that the synchronization in small-world networks may be realized more easily. Key words Lyapunov exponent - chaotic synchronization - small-world networks MSC 2000 37D45 Project supported by the National Natural Science Foundation of China(Grant No. 10171061)
基金Project supported by the National Natural Science Foundation of China (Grant No 60274032) and the Science and Technology Rising-Star Program of Shanghai (Grant No 04QMH1405).
文摘A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively. This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.
文摘A new kind of secure communication system which combines the chaotic encryption means with the conventional encryption method is discussed. With the analysis results and the experiment data, the anti-attack ability of this communication system is significantly improved compared to that of the either method. At the same time, a new method of chaotic synchronization is proposed. With a small mixed discrete chaotic signal, it is quickly to synchronize the communication and a good security performance is ensured.
基金supported by the National Natural Science Foundation of China (Grant No. 10901145)
文摘This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.
基金Project supported by the National Natural Science Foundation of China (Grant No 10726042)Youth Science Foundation of Shanxi Normal University
文摘This paper detects and characterizes the diverse roles played by bounded noise in chaotic phase synchronization (CPS) of weakly coupled nonlinear stochastic systems. Analysis of a paradigmatic model of two bidirectional coupled three-level food chains is carried out by various statistical measures such as Shannon entropy and mutual information. The results indicate that inside the synchronous regime, CPS is considerably reduced under the influence of bounded noise; near the onset of phase synchronization, temporal phase locking is diversely changed with the increase of noise, i.e., either weak or strong noise also degrades the degree of CPS, while intermediate noise enhances CPS remarkably, and an optimal noise intensity is detected that maximizes the enhancement.
文摘A new synchronization scheme for chaotic(hyperchaotic) maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features:(i) it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;(ii) it is rigorous,being based on theorems;(iii) it can be readily applied to any chaotic(hyperchaotic) maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map(as the drive system) and the three-dimensional hyperchaotic Wang map(as the response system),and the three-dimensional H′enon-like map(as the drive system) and the two-dimensional Lorenz discrete-time system(as the response system).
基金supported by the National Natural Science Foundation of China (Grant Nos 60777041 and 60577019)the International Cooperation Project of Shanxi Province,China (Grant No 2007081019)
文摘This paper numerically investigates the effects of dispersion on optical fibre chaotic communication, and proposes a dispersion compensation scheme to improve the performance of optical fibre chaotic communication system. The obtained results show that the transmitter-receiver synchronization progressively degrades and the signal-to-noise ratio of the recovered message deteriorates as the fibre length increases due to the dispersion accumulation. Two segments of 2.5-km dispersion-compensating fibres are symmetrically placed at both ends of a segment of 245-km nonzero dispersionshifted fibre with low dispersion in one compensation period. The numerical results show that the signal-to-noise ratio of the extracted 1 GHz sinusoidal message is improved from -2.92 dB to 15.38 dB by this dispersion compensation for the transmission distance of 500 km.
基金This work was financially supported by the National Nature Science Foundation of China (No. 69772014)
文摘The theories of synchronization based on secure communications using digital chaos are presented. A new synchronous method-cycles-interval Pulse drive is developed and realized. Experimental results show it is available, and in order to reduce synchronous noise, a method using model references solves the ratio of signal power to noise power, so the secure communication system can be realized.
基金Project supported by the National Natural Science Foundation of China(Grant No10372054)the Science Foundation of Jiangnan University,China(Grant No000408)
文摘The adaptive coupled synchronization method for non-autonomous systems is proposed. This method can avoid estimating the value of coupling coefficient. Under the uniform Lipschitz assumption, we derive the asymptotical synchronization for a general coupling ring network with N identical non-autonomous systems~ even when N is large enough. Strict theoretical proofs are given. Numerical simulations illustrate the effectiveness of the present method.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10372054 and 70431002.
文摘We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-adaptive mechanism correctly represents essential characteristics of self-adaptation in complex systems. We also show that this method is reasonable both from the coupling viewpoint in physics and from the controller design viewpoint in control theory.
基金Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No BK2001138).
文摘The digital communication of two-dimensional messages is investigated when two solid state multi-mode chaotic lasers are employed in a master-slave configuration. By introducing the time derivative of intensity difference between the receiver (carrier) and the transmittal (carrier plus signal), several signals can be encoded into a single pulse. If one signal contains several binary bits, two-dimensional messages in the form of a matrix can be encoded and transmitted on a single pulse. With these improvements in secure communications using chaotic multi-mode lasers, not only the transmission rate can be increased but also the privacy can be enhanced greatly.
文摘A novel La Shalle's invariant set theory (LSIST) based adaptive asymptotic synchronization (LSISAAS) method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are considered as system states. The LSISASS strategy depends on the only information, i.e. one state of the master system. According to the LSIST, the LSISASS method can asymptotically synchronize fully the states of the master system and the unknown system parameters as well. Simulation results also validate that the LSISAAS approach can obtain asymptotic synchronization.
文摘A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its (q-order and 2q-order) time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its (q-order and 2q-order) time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61273088,10971120,and 61001099)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2010FM010)
文摘To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors (CMPS) of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.
基金supported by the National Natural Science Foundation of China(Grant No.11875135)Fundamental Research Funds for National University,China University of Geosciences(Wuhan)(Grant No.CUGGC05)。
文摘The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively.However,the coupled oscillators in practice are nonidentical,and there exist mismatched parameters.It has been proved that under certain conditions,complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points,yet other cooperative behaviors are not addressed.In this paper,we further consider two coupled nonidentical oscillators with the same equilibrium points,where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors.We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings.In the case of directed coupling,death islands appear in two-parameter spaces.The mechanism inducing these transitions is presented.
文摘This paper has designed 2-channel dense wavelength division multiplexing (DWDM) chaotic sys- tem at the frequencies of 193.1 and 193,2THz, respec- tively. The optical chaotic signals were produced by using the semiconductor laser that is numerically modeled by employing laser rate equations. These two channels were multiplexed and then propagated through single mode optical fiber (SMF) of 80kin length with dispersion compensating fiber of 16 km length. Erbium doped fiber amplifier (EDFA) was used to compensate the power losses in the SMF. In lhis paper, we investigated the effects of polarization mode dispersion (PMD) and nonlinearities especially stimulated Raman scattering (SRS) on 2 channel DWDM chaotic communication system by varying the length of the SMF and value of differential group delay (DGD).
基金the National Natural Science Foundation of China(Grant No.61773010)。
文摘Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.