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...

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...

The returns and risks of investment portfolio in stock market crashes are investigated by considering a theoretical model, based on a modified Heston model with a cubic nonlinearity, proposed by Spagnolo and Valenti. Through numerically simulating probability density function of returns and the...

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 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 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...

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...

A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value (〈x〉st) and normalized varianceλ2 of the tumor cell population and state transition rate (κ)...

The effects of correlations between additive and multiplicative noises on the state variable correlation function of a bistable system driven by cross-correlated noises were studied. Applying an approximate Fokker–Planck equation to the system, the analytic expression for the state variable...

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...