Quantum key distribution with blind polarization bases.

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.

Encryption with synchronized time-delayed systems.

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.

Synchronization of chaotic oscillators due to common delay time modulation.

We have found a synchronization behavior between two identical chaotic systems when their delay times are modulated by a common irregular signal. This phenomenon is demonstrated both in two identical chaotic maps whose delay times are driven by a common chaotic or random signal and in two identical chaotic oscillators whose delay times are driven by a signal of another chaotic oscillator. We analyze the phenomenon by using the Lyapunov exponents and discuss it in relation to generalized synchronization.

Effects of time-delayed feedback on chaotic oscillators.

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 Rössler 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 Rössler 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.

Characteristics of a delayed system with time-dependent delay time.

The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate that 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.

Chaotic behaviors of operational amplifiers.

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.

Experimental observation of characteristic relations of type-III intermittency in the presence of noise in a simple electronic circuit.

We investigate the characteristic relations of type-II and -III intermittencies in the presence of noise. The theoretically predicted characteristic relation is that approximately exp[/epsilon/(2)] for a negative regime of epsilon and approximately epsilon(-nu) for the positive regime of epsilon (1/2 is the average laminar length and (1+epsilon) is the slope of the local Poincaré map around the tangent point. We experimentally confirm these relations in a simple electronic circuit.

Periodic phase synchronization in coupled chaotic oscillators.

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.

Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers.

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.

Generalized phase synchronization in unidirectionally coupled chaotic oscillators.

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 and clarify its characteristics using Lyapunov exponents and phase difference plots.

Sequential synchronization of chaotic systems with an application to communication.

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.