The auto-correlation function and the cross-correlation function of an autonomous stochastic system with time delays are investigated. We obtain the distribution curves of the auto-correlation function Cx(s) and Cy(s), and the cross-correlation function Cxy(s) and Cyx(s) of the stochastic...

The roles of extrinsic periodic information on the stability of stock price for the case of the stock market crashes are investigated with Heston model. From numerical simulation of the mean escape time (MET), the results indicate that: (i) the varying amplitude of extrinsic periodic information...

The returns and risks of investment portfolio in a financial system was investigated by constructing a theoretical model based on the Heston model. After the theoretical model and analysis of portfolio were calculated and analyzed, we find the following: (i) The statistical properties (i.e., the...

Immunotherapy is one of the most recent approaches in cancer therapy. A mathematical model of tumor–immune interaction, subject to a periodic immunotherapy treatment (imitated by a periodic signal), correlative and bounded stochastic fluctuations and time delays, is investigated by numerical...

The transport properties of an active Brownian particle with a time-delayed feedback and an external bias are investigated theoretically. By virtue of the perturbation theory for small delay, analytical expressions for the mean velocity and effective diffusion coefficient are derived. There...

The effects of the delay time on the stability of a market model are investigated, by using a modified Heston model with a cubic nonlinearity and cross-correlated noise sources. These results indicate that: (i) There is an optimal delay time τo which maximally enhances the stability of the...

A model of tumor–immune system interplay with time delays and cross-correlated sine-Wiener noises is investigated by numerical simulations for the stationary probability distribution (SPD) and stationary mean value 〈x〉st of tumor cell population. Results show that (i) the structure of the...

Stochastic resonance (SR) induced by the bounded noise in an asymmetric bistable system is investigated. Based on stochastic simulation, the signal power amplification SPA is derived for the case of the additive modulated signal. The simulation results indicate that: (1) the SR phenomenon is...

The stochastic resonance in an underdamped quartic double-well potential with time delayed feedback is studied numerically. The signal power amplification is employed to characterize the stochastic resonance of the system. Simulation results indicate that: (i) for moderate frequency of the...

The effects of strong noise on the decline and propagation processes of a population in the Malthus–Verhulst model with time delay are investigated by a stochastic simulation. Time delays in two different processes are concurrent in ecosystems. The simulation results indicate that: The...