[en] In this paper, we attempt to provide a solution for the fractional linear complementarity problem related to the evaluation of American put option generated by the fractional Heston stochastic volatility model. Using the Adomian decomposition, a numerical investigation is conducted to confirm the theoretical results. (author)

[en] We investigate in detail the nonlinear and chaotic dynamics of the Colpitts oscillator. We show that we can control the dynamics of the oscillator by either inductors, capacitors or resistors in the emitter or collector network. We find the bifurcation diagram and the Lyapunov exponent of the oscillator and investigate them. We also find bifurcation diagram in 2D space when two parameters from the mentioned parameters are variables. The 2D diagram shows the nonlinear behaviour of the system more clearly. (author)

[en] In this study, the system with fractional power nonlinearity is introduced into the theory of aperiodic stochastic resonance (ASR). The fractional exponent is a key parameter and its effect on the ASR phenomenon excited by aperiodic binary signal is investigated in this system. Compared to the classical bistable system, the system with fractional power nonlinearity shows better performance. It can adjust not only the noise intensity but also the fractional exponent to enhance weak signal. In the field of signal transmission, pure aperiodic binary signal is usually submerged in the noise and the signal is unknown. Thus, an effective method is proposed based on ASR and moving average. By the method, the unknown aperiodic binary signal can be recovered in the noise background.To improve the efficiency of the signal recovery, the adaptive ASR is realised with the help of adaptive particles warm optimisation (APSO) algorithm to optimise the parameters.The method may provide some reference to the engineering field. (author)

[en] Noise improves the reliability of logic operations if noise parameter is in certain proper region (reliable region), which is known as logical stochastic resonance (LSR). LSR attracts much attention due to its potential application in new-style logic devices. However, nothing is reported about the effect of cross-correlated sine-Wiener (CCSW) bounded noises on the reliability and agility of logic operations. Here we explicitly demonstrate that in certain proper parameter regions of amplitude and correlation time of CCSW noises, CCSW noises can induce LSR. In addition, cross-correlation intensity of CCSW noises can drastically influence the range of reliable region. By comparison, moderate cross-correlation intensity can drastically destroy the reliability of the logic system, and strongly shrink the optimal parameter ranges, depending on cross-correlation time and amplitude. Moreover, for given amplitudes and cross-correlation time, a little faster logic operation can be obtained with increasing cross-correlation intensity. (author)

[en] The characteristic of a monostable stochastic resonance system driven by time-delayed feedback is investigated. Under the small-delay approximation theory, the effective potential function of the system is obtained and the influence of system parameters on the shape of the potential function is also discussed. Furthermore, we consider the influence of the input signal on the system and derive the asymmetric bistable potential function. By using the adiabatic approximation theory and the two-state theory, the theoretical expressions of the steady-state probability distribution function, mean first-passage time and signal-to-noise ratio are obtained, which are three excellent metrics to measure the performance of system. Simulation results show that the parameters A, a and τ can motivate the SR phenomenon while β suppresses the SR phenomenon. At last, the numerical simulation results obtained from the original Langevin equation and the effective Langevin equation can verify whether the theoretical derivation is correct. (author)