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A new encoding scheme for information transfer with modulated delay time in a time-delay system is proposed. In the scheme, the message is implicitly encoded into the modulated delay time. The information transfer rate as a function of encoding redundancy in various noise scales is presented and it is analyzed that the implicit encoding scheme (IES) has stronger resistance against channel noise than the explicit encoding scheme (EES). In addition, its advantages in terms of secure communication and feasible applications are discussed.

We propose an efficient key scheme, which can generate a great number of communication keys, for communication using chaos synchronization. We have attained the keys from delay times of time-delay coupled chaotic systems. We explain the scheme and the efficiency by coupling Henon and logistic maps and illustrate them by coupling Navier–Stokes and Lorenz equations as a continuous system.

We have developed a stabilization method of quasi-periodicity based on a return map. The method is explained in the forced Van der Pol oscillator, and applied experimentally to a quasi-periodic output of a Q-switched Nd:YAG laser. Even though the attractors have no unstable periodic orbit, we were able to stabilize them to an arbitrarily chosen orbit by targeting the trajectory into it.

We have observed anti-synchronization phenomena in coupled identical chaotic oscillators. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. We have qualitatively analyzed its base mechanism by using the dynamics of the difference and the sum of the relevant variables in coupled chaotic oscillators. Near the threshold of the synchronization and anti-synchronization transition, we have obtained the novel characteristic relation.

We analyze QED3 with a scalar-scalar type four-fermion interaction in the framework of 1/N expansion. We have derived the Dyson-Schwinger gap equation up to the next-to-leading order and determined the dynamically generated fermion mass as a function of the number of fermion flavors N and a scaled coupling θ. We observe that the critical behaviors are separated by the point [Formula: see text] and, contrary to the leading behaviors, there are mass generations even when θ ≥ θc with the critical flavor Nc. The critical line on the Nc−θc plane is presented. We also discuss the vacuum stability of our model, and confirm that our nontrivial solutions are energetically preferred to the perturbative solution Σ(p)=0.

We study the dynamics of the motion of a metallic particle bouncing between alternating high-voltage electrodes in a compressed SF6 gas coaxial insulator. Through the study of the bifurcation diagram and attractors, we find that the dynamics of a metallic particle develops from a stable periodic motion to chaos as the strength of the electric field increases. Based on these results, we show numerically that the chaotic motion of the particle can be stabilized by using a chaos control method.

Using the real-time formalism we derive the temperature dependent gap equation for a dynamically generated fermion mass of ladder QED with four-fermion interaction. We obtain the value of the critical temperature from the gap equation. Some numerical results are presented. We also consider the composite operator effective potential of this model.

We examine the recently proposed minimal chiral Schwinger model with the new Wess-Zumino action. From the physical requirement, we restrict the regularization ambiguity and show that it is equivalent to the Schwinger model.

An anomalous gauge theory can be quantized consistently by perturbation theory instead of Dirac's method in the Hamiltonian formulation. It reveals the gradually varying commutator structures according to the higher-order vertex corrections and the series sum of the commutator algebra of each order becomes the Dirac brackets for the bosonized action. However, the perturbation approach in the Lorentz-invariant gauge does not give the Dirac brackets.

We propose a new protocol for quantum key distribution without basis reconciliation. We show that the security level of the protocol against photon number splitting (PNS) attack is enhanced, relative to the BB84 protocol.

The phase difference in coupled chaotic oscillators exhibits a small noiselike fast fluctuation in long-term phase dynamics. The fast fluctuation can cause an error in the measurement of the period of the temporary phase locking state. We discuss why we should filter out the fast fluctuation on determination of periodic phase synchronization.

In this paper, we briefly show how the quantum key distribution with blind polarization bases [Kye et al., Phys. Rev. Lett. 95, 040501 (2005)] can be made secure against the impersonation attack.

We propose a new quantum key distribution scheme that uses the blind polarization basis. In our scheme the sender and the receiver share key information by exchanging qubits with arbitrary polarization angles without basis reconciliation. As only random polarizations are transmitted, our protocol is secure even when a key is embedded in a not-so-weak coherent-state pulse. We show its security against the photon number splitting attack and the impersonation attack., Comment: Security has been improved upon referee's comment. 4 pages and 2 figures

We propose a new communication scheme that uses time-delayed chaotic systems with delay time modulation. In this method, the transmitter encodes a message as an additional modulation of the delay time and then the receiver decodes the message by tracking the delay time. We demonstrate our communication scheme in a system of coupled logistic maps. Also we discuss the error of the transferred message due to an external noise and present its correction method.

We investigate the origin of the transition inside the desynchronization state via phase jumps in coupled chaotic oscillators. We claim that the transition is governed by type-I intermittency in the presence of noise whose characteristic relation is $ \propto \exp(\alpha|\epsilon_t -\epsilon|^{3/2})$ for $\epsilon_t -\epsilon \propto (\epsilon_t -\epsilon)^{-1/2}$ for $\epsilon_t -\epsilon >0$, where $$ is the average length of the phase locking state and $\epsilon$ is the coupling strength. To justify our claim we obtain analytically the tangent point, the bifurcation point, and the return map which agree well with those of the numerical simulations., Comment: 11 pages, 4 figures

We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are driven by correlated (but not identical) inputs from the drive oscillator. We call this phenomenon Generalized Phase Synchronization (GPS) and clarify its characteristics using Lyapunov exponents and phase difference plots., 4 pages, 5 figures

We study the effects of time-delayed feedback on chaotic systems where the delay time is both fixed (static case) and varying (dynamic case) in time. For the static case, typical phase coherent and incoherent chaotic oscillators are investigated. Detailed phase diagrams are investigated in the parameter space of feedback gain ( K ) and delay time ( tau ). Linear stability analysis, by assuming the time-delayed perturbation, varies as e(lambdat) where lambda is the eigenvalue, gives the boundaries of the stability islands and critical feedback gains ( K(c) ) for both Rossler oscillators and Lorenz oscillators. We also found that the stability island are found when the delay time is about tau= (n+ 1 / 2 ) T , where n is an integer and T is the average period of the chaotic oscillator. It is shown that these analytical predictions agree well with the numerical results. For the dynamic case, we investigate Rossler oscillator with periodically modulated delay time. Stability regimes are found for parameter space of feedback gain and modulation frequency in which it was impossible to be stabilized for a fixed delay time. We also trace the detailed routes to the stability near the island boundaries for both cases by investigating bifurcation diagrams.

We have found a synchronization behavior between two identical chaotic systems^M when their delay times are modulated by a common irregular signal. ^M This phenomenon is demonstrated both in two identical chaotic maps whose delay times are driven by a common^M chaotic or random signal and in two identical chaotic oscillators whose delay times are driven by^M a signal of another chaotic oscillator. We analyze the phenomenon by using^M the Lyapunov exponents and discuss it in relation with generalized synchronization.^M, Comment: 5 pages, 4 figures (to be published in PRE)

The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate the nonlinearity characteristics of the time-delayed system are significantly changed depending on the properties of time-dependent delay time and especially that the reconstructed phase trajectory of the system is not collapsed into simple manifold, differently from the delayed system with fixed delay time. We discuss the possibility of a phase space reconstruction and its applications., Comment: 4 pages, 6 figures (to be published in Phys. Rev. E)

We investigate nonlinear dynamical behaviors of operational amplifiers. When the output terminal of an operational amplifier is connected to the inverting input terminal, the circuit exhibits period-doubling bifurcation, chaos, and periodic windows, depending on the voltages of the positive and the negative power supplies. We study these nonlinear dynamical characteristics of this electronic circuit experimentally.

We investigate the characteristic relations of type-II and -III intermittencies in the presence of noise. The theoretically predicted characteristic relation is that $〈\mathcal{l}〉\ensuremath{\sim}\mathrm{exp}{|\ensuremath{\epsilon}{|}^{2}}$ for a negative regime of \ensuremath{\epsilon} and $〈\mathcal{l}〉\ensuremath{\sim}{\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\nu}}$ for the positive regime of \ensuremath{\epsilon} $(1/2l~\ensuremath{\nu}l1),$ where $〈\mathcal{l}〉$ is the average laminar length and $(1+\ensuremath{\epsilon})$ is the slope of the local Poincar\'e map around the tangent point. We experimentally confirm these relations in a simple electronic circuit.

Using mutually coupled nonidentical continuous-wave Nd:YAG lasers, we experimentally confirmed the recently proposed transition route from phase synchronization to complete synchronization. As evidence of this transition we obtained the probability distribution of the intermittent synchronization time near the threshold of the complete synchronization transition.

We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic appearance of temporal phase locking state and that the state leads to local negativeness in one of the vanishing Lyapunov exponents. By taking a statistical measure, we present the evidences of the phenomenon in unidirectionally and mutually coupled chaotic oscillators, respectively. And it is qualitatively discussed that the phenomenon is described by a nonuniform oscillator model in the presence of noise., 4 pages, 4 figures. submitted to Phys. Rev. E. The typo in Eq.(1) has been fixed

We have observed various synchronous motions between laser spots of TEM10 mode in a diode laser pumped Nd:YAG laser. The dynamics of TEM10 mode develop from synchronous motion to anti-synchronous motion through intermittent jumps between the two motions as the pumping increases. We analyze the phenomena experimentally.

We investigate synchronization in the presence of delay time modulation for application to communication. We have observed that the robust synchronization is established by a common delay signal and its threshold is presented using Lyapunov exponents analysis. The influence of the delay time modulation in chaotic oscillators is also discussed., Comment: 9 pages, 6 figures

We propose a hierarchically structured communication system by using sequentially synchronized chaotic systems. Sequential synchronization is attained by first feeding a noiselike signal to a variable of the first transmitter and its receiver simultaneously and then feeding a variable of the first transmitter and its receiver to a variable of the second transmitter and its receiver, respectively, for subsequent feedings of variables in sequence. When this is applied to communication, the hierarchical structure enables selective protection of information due to the sequential property. We illustrate this in sequentially synchronized Navier-Stokes and Lorenz equations.

The general structure of two-dimensional intermittency is discussed. The structure of channel and the trajectory in the return map are compared with those of one-dimensional intermittency and the scaling relations are obtained according to the trajectory. We illustrate the temporal behavior and scaling relations in a coupled map. The numerical results agree well with the theoretical predication of approximately equal 1/sqrt[epsilon].

We analyze the bifurcation of an attractor in a system of multiplicatively coupled maps. It is shown that the phenomenon can be characterized by on-off intermittency and it is rigorously described by the on-off intermittency in the presence of noise through the concept of a virtually invariant manifold. Presenting numerical results which conform our claims, we elucidate the role of on-off intermittency in bifurcation phenomena.

Near a phase synchronization region, the phase difference of two coupled chaotic oscillators exhibits phase jumps. For an example, the coupled Rossler oscillators exhibit 2π jumps, which is explained by using a potential shape of the phase related with type-I intermittency in the presence of noise. But, in our study, the two coupled hyperRossler oscillators exhibit ±2π jumps, which can not be explained in the previous way. So we suggest a general method to analyze the phenomenon which uses the return map of the phase equation and present the scaling relation of the phase jumps by using the scaling properties of the laminar length of intermittency in the presence of noise.

Near the point of tangent bifurcation, the scaling properties of the laminar length of type-I intermittency are investigated in the presence of noise. Based on analytic and numerical studies, we show that the scaling relation of the laminar length is dramatically deformed from $\frac{1}{\sqrt{\epsilon}}$ for $\epsilon >0$ to $\exp\{\frac{1}{D}|\epsilon|^{3/2}\}$ for $\epsilon, Comment: 4 pages, 4 figures

We study the phase synchronization (PS) with type-II intermittency showing $\pm 2 \pi$ irregular phase jumping behavior before the PS transition occurs in a system of two coupled hyperchaotic R\"{o}ssler oscillators. The behavior is understood as a stochastic hopping of an overdamped particle in a potential which has $2 \pi$-periodic minima. We characterize it as type-II intermittency with external noise through the return map analysis. In $\epsilon_{t} < \epsilon < \epsilon_{c}$ (where $\epsilon_{t}$ is the bifurcation point of type-II intermittency and $\epsilon_{c}$ is the PS transition point in coupling strength parameter space), the average length of the time interval between two successive jumps follows $ \sim \exp(\mid\epsilon_{t} - \epsilon\mid^{2})$, which agrees well with the scaling law obtained from the Fokker-Planck equation., Comment: 5 pages, 5 figures

We analyze (2+1)-dimensional Gross-Neveu model with a Thirring interaction, where a vector-vector type four-fermi interaction is on equal terms with a scalar-scalar type one. The Dyson-Schwinger equation for fermion self-energy function is constructed up to next-to-leading order in 1/N expansion. We determine the critical surface which is the boundary between a broken phase and an unbroken one in ($\alpha_c,~ \beta_c,~ N_c$) space. It is observed that the critical behavior is mainly controlled by Gross-Neveu coupling $\alpha_c$ and the region of the broken phase is separated into two parts by the line $\alpha_c=\alpha_c^*(=\frac{8}{\pi^2})$. The mass function is strongly dependent upon the flavor number N for $\alpha > \alpha_c^*$, while weakly for $\alpha \alpha_c^*$, the critical flavor number $N_c$ increases as Thirring coupling $\beta$ decreases. By driving the CJT effective potential, we show that the broken phase is energetically preferred to the symmetric one. We discuss the gauge dependence of the mass function and the ultra-violet property of the composite operators.

We study dynamical chiral symmetry breaking in (2+1)-dimensional QED with a Chern-Simons term. It is observed that the Chern-Simons term improves the infrared behavior of the photon propagator and enables one to investigate chiral symmetry breaking by the ladder Dyson-Schwinger equation without the infrared divergence problem. The model shows the dynamical mass generation only when [alpha][prime][gt]1/2 and the dynamically generated mass is linearly proportional to the coupling [alpha][prime]. We also determine the dynamically generated mass at finite temperature and the critical temperature above which chiral symmetry is restored. The critical line which separates the two phases U(2) and [direct product]U(1) is presented on the ([alpha][prime],[ital T][prime]) plane.

We investigate the one-loop effective potential of the supersymmetric model in the high-temperature domain. We observe the fact that supersymmetry can be broken by finite-temperature effects and there is a possibility that broken supersymmetry can be restored in the higher-temperature region

We investigate the critical behavior of the sine-Gordon theory at the one-loop level. We observe that the theory has a critical temperature {beta}{sub {ital c}} and restores the symmetry above {beta}{sub {ital c}}.

We derive another Wess-Zumino (minimal WZ) action which cancels the gauge anomaly of the chiral Schwinger model following a recently suggested method. The new WZ action cancels the gauge anomaly for {alpha}=1 and its effective action is equivalent to the usual one for {ital a}=2.

We experimentally stabilize a chaotic output of a diode-laser-pumped Nd:yttrium–aluminum–garnet laser by using oscillation quenching. When the chaotic laser is mutually coupled with a Rossler oscillator that is implemented by an electronic circuit, both chaotic systems are stabilized to steady states. We experimentally study the route to the steady states as the coupling strength increases, and numerically confirm the route by coupling Lorenz and Rossler oscillators mutually.

We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics.