[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] 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] 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)

[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] 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] We investigate ultracold magnetic-field-assisted collisions in the so far unexplored ErYb system. The nonsphericity of the Er atom leads to weakly anisotropic interactions that provide the mechanism for Feshbach resonances to emerge. The resonances are moderately sparsely distributed with a density of 0.1–0.3 G⁻¹ and exhibit chaotic statistics characterized by a Brody parameter η ≈ 0.5–0.7. The chaotic behaviour of Feshbach resonances is accompanied by strong mixing of magnetic and rotational quantum numbers in near-threshold bound states. We predict the existence of broad resonances at fields < 300 G that may be useful for the precise control of scattering properties and magnetoassociation of ErYb molecules. The high number of bosonic Er–Yb isotopic combinations gives many opportunities for mass scaling of interactions. Uniquely, two isotopic combinations have nearly identical reduced masses (differing by less than 10⁻⁵ relative) that we expect to have strikingly similar Feshbach resonance spectra, which would make it possible to experimentally measure their sensitivity to hypothetical variations of proton-to-electron mass ratio. (paper)

[en] We compare the entire classical and quantum evolutions of the Dicke model in its regular and chaotic domains. This is a paradigmatic interacting spin-boson model of great experimental interest. By studying the classical and quantum survival probabilities of initial coherent states, we identify features of the long-time dynamics that are purely quantum and discuss their impact on the equilibration times. We show that the ratio between the quantum and classical asymptotic values of the survival probability serves as a metric to determine the proximity to a separatrix in the regular regime and to distinguish between two manifestations of quantum chaos: scarring and ergodicity. In the case of maximal quantum ergodicity, our results are analytical and show that quantum equilibration takes longer than classical equilibration. (paper)

[en] The phenomenology of reconnection events, associated to relaxations in high-current (∼1.5 MA) plasmas of the reversed-field pinch device RFX–mod, is shown. Each relaxation event can be described as a series of stages starting in the core and propagating towards the plasma edge. In an initial stage (trigger), the evolution of the q profile brings resonant layers closer together, allowing for an interaction of the current sheets associated to tearing modes at the respective rational values of q. The phase locking of the resonant modes then initiates the reconnection process that, once started, changes the magnetic topology bringing the initially helical state to a more chaotic configuration. (paper)

[en] We have studied the shadows of a Schwarzschild black hole surrounded by a Bach–Weyl ring through the backward ray-tracing method. The presence of Bach–Weyl ring leads to that the photon dynamical system is non-integrable and then chaos would appear in the photon motion, which affects sharply the black hole shadow. The size and shape the black hole shadow depend on the black hole parameter, the Bach–Weyl ring mass and the Weyl radius between black hole and ring. Some self-similar fractal structures also appear in the black hole shadow, which originates from the chaotic lensing. We also study the change of the image of Bach–Weyl ring with the ring mass and the Weyl radius. Finally, we analyze the invariant manifolds of Lyapunov orbits near the fixed points and discuss further the formation of the shadow of a Schwarzschild black hole with Bach–Weyl ring.

[en] In this study, we present a new method for assessing the functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch. This method is based on the footprint of the drive oscillator on the response oscillator. Specifically, we calculate the magnitude squared coherence between the intrinsic frequency of the drive oscillator and the oscillation frequency of the dynamics of the spectral energy of the response oscillator. The spectral energy of the response oscillator is estimated using a modified S-transform algorithm with a short sliding window. We apply the proposed approach to master–slave Rössler systems and coupled Van der Pol oscillators with a frequency ratio of ∼ 1:4 and show that when the slave signal is contaminated with white Gaussian noise at different signal-to-noise ratios (SNR), the new algorithm is well suited to assess the presence of coupling with a priori known direction in noisy, unidirectionally coupled chaotic oscillators, especially in the case of weak and moderate coupling. (author)