Dynamics of erbium-doped fibre laser with optical delay feedback and chaotic synchronization

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.

Secure communication by generalized chaotic synchronization

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.

Chaotic Synchronization for Dynamical System Constructed on Star Network

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)

Chaotic synchronization via linear controller

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.

Implementation of a new chaotic encryption system and synchronization

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.

Synchronization between two different chaotic systems with noise perturbation

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.

Study on phase synchronization of stochastic chaotic system

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.

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

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）.

Prescribed performance synchronization for fractional-order chaotic systems

In this paper the synchronization for two different fractional-order chaotic systems, capable of guaranteeing synchronization error with prescribed performance, is investigated by means of the fractional-order control method. By prescribed performance synchronization we mean that the synchronization error converges to zero asymptotically, with convergence rate being no less than a certain prescribed function. A fractional-order synchronization controller and an adaptive fractional-order synchronization controller, which can guarantee the prescribed performance of the synchronization error,are proposed for fractional-order chaotic systems with and without disturbances, respectively. Finally, our simulation studies verify and clarify the proposed method.

Impulsive synchronization and control of directed transport in chaotic ratchets

The impulsive synchronization problem of two identical chaotic ratchets is investigated in this paper. We demonstrate that the impulsive method to control directed transport is applicable when there are multiple co-existing attractors in phase space transporting particles in different directions. Numerical simulations are carried out to illustrate the effectiveness of the proposed method.

Improving performance of optical fibre chaotic communication by dispersion compensation techniques

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.

Synchronization of Digital Chaos in Secure Communication Systems

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.

Adaptive coupled synchronization of non-autonomous systems in ring networks

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.

Digital communication of two-dimensional messages in a chaotic optical system

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.

La Shalle＇s invariant-set-theory based asymptotic synchronization of duffing system with unknown parameters

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.

A specific state variable for a class of 3D continuous fractional-order chaotic systems

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.

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

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.

Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points

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.

Impact of polarization mode dispersion and nonlinearities on 2-channel DWDM chaotic communication systems

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）.

Dynamics and synchronization of a complex-valued star network

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.