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Like numerous complex dynamical systems, financial systems generate abrupt transitions which can cause financial crisis. Since the state of the system generally exhibits little change before such transitions, the sudden transitions are difficult to anticipate. There are considerable literatures for the construction of early warning signals based on features of time series, but there is essential lack of investigating effects of early warning signals at spatial structure for the financial systems. This paper aims at investigating the spatially extended endogenous credit system with stochasticity using spatial early warning signals. First, we apply patch-size distribution to predict upcoming critical transition. The results show that the patch-size distribution conforms a power law at threshold. Second, we also predict impending critical transition utilizing the spatial early-warning indicators widely applied on dynamical systems. These indicators predict successfully the critical transition between high and low asset price state. To enhance the robustness of early warning, we use these methods together to detect impending transition. We hope that our methods can promote the utilization and test of spatial early warning signals on real financial systems. • Patch-size distribution conforms a power law when system reaches threshold. • All indicators detect warning signals before system reaching a new state. • Our research provides a new perspective on study of complex financial systems. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical properties in a foraging colony system with time delay and non-Gaussian noise were investigated. Using delay Fokker–Planck approach, the stationary probability distribution (SPD), the associated relaxation time (ART) and normalization correlation function (NCF) are obtained, respectively. The results show that: (i) the time delay and non-Gaussian noise can induce transition from a single peak to double peaks in the SPD, i.e., a type of bistability occurring in a foraging colony system where time delay and non-Gaussian noise not only cause transitions between stable states, but also construct the states themselves. Numerical simulations are presented and are in good agreement with the approximate theoretical results; (ii) there exists a maximum in the ART as a function of the noise intensity, this maximum for ART is identified as the characteristic of the non-Gaussian noise-weakened stability of the foraging colonies in the steady state; (iii) the ART as a function of the noise correlation time exhibits a maximum and a minimum, where the minimum for ART is identified as the signature of the non-Gaussian noise-enhanced stability of the foraging colonies; and (iv) the time delay can enhance the stability of the foraging colonies in the steady state, while the departure from Gaussian noise can weaken it, namely, the time delay and departure from Gaussian noise play opposite roles in ART or NCF. [ABSTRACT FROM AUTHOR]

Considering time delays in the deterministic and stochastic forces, we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem. The stationary probability distribution (SPD) and mean first passage time (MFPT) are obtained, respectively. Our main results show: (i) The multiplicative noise, positive cross-correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one, but the additive noise and negative cross-correlation can induce the regime shifts from the bust outbreak state to the boom one; (ii) For the negative cross-correlation, the MFPT as a function of noise strengths exhibits one maximum, which shows the characteristic of the noise-delayed switching for the boom outbreak state, but for the no cross-correlation or positive cross-correlation, the MFPT decreases with the noise strengths; (iii) Two different types of time delays play same roles on the maximal MFPT with additive noise, and play opposite roles on the maximal MFPT with multiplicative noise. The mechanisms for noises-and delays-induced regime shifts between two states can be explained physically through the effective potential of ecological model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the transport of an inertial Brownian motor moving in an asymmetric periodic potential, where it is driven by a time periodic and a constant biasing driving force, and potential fluctuations generated by a Gaussian white noise. It is found that some anomalous transports (ATs) appear in the presence of the potential fluctuations. For smaller potential fluctuations, we detect that the phenomenons of absolute negative mobility (ANM) near zero bias, and negative nonlinear mobility (NNM) at larger bias away from equilibrium, which means that the inertial Brownian motor moves opposite to the bias force in the two parameter regimes. However for larger potential fluctuations, the phenomenons of both the ANM and NNM vanish. Furthermore, the asymmetry of the potential can also cause the ATs (i.e., both ANM and NNM) to disappear. [Copyright &y& Elsevier]

Abstract: We study the effect of time delay in the FitzHugh–Nagumo neural model with correlations between multiplicative and additive noise terms. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function (SPDF), the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) are obtained, respectively. Research results show that: (i) the system undergoes a succession of two phase transitions (i.e., the reentrance phenomenon) as the noise correlation parameter is increased and a (single) phase transition as the time delay is increased. (ii) The MFPT as a function of the multiplicative noise intensity exhibits a maximum. This maximum for MFPT identifies the noise enhanced stability (NES) effect, the noise correlation parameter intensifies the NES effect while the time delay, and the additive noise intensity weakens it. (iii) The existence of a maximum in the SNR as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance (SR) phenomenon, the noise correlation parameter enhances the SR while the time delay, and the additive noise intensity weaken it. [ABSTRACT FROM AUTHOR]

Abstract: Transport of an inertial Brownian motor moving in an asymmetric periodic potential driven by an external force and correlated noises is investigated. Using the numerical algorithm, the asymptotic mean velocity (AMV) for characterizing directed transport is obtained. The effects of the external driving force and the correlation between the two noises on the AMV are discussed. The results manifest: (1) the external driving force and the correlation between the two noises can lead to the phenomena like current reversal. (2) The competitions among the external driving force and the correlation between the two noises are necessary for current reversal, i.e., . (3) Different directions of transport are found for different masses of the Brownian particles under the condition . Therefore a theoretical study is suggested for separating Brownian particles according to their different masses in the ratchet system. [Copyright &y& Elsevier]

The second-order algorithm for simulating stochastic differential equations with Gaussian white noises is presented. These stochastic differential equations are universal type, among, these Gaussian white noises come from different sources. Specifically, the proposed algorithm extends previous first-order algorithm for stochastic differential equations with different white noises and second-order algorithm for stochastic differential equations with same white noise. In practice, it is proved that this algorithm is scientific. • The second-order algorithm for simulating universal SDEs with Gaussian white noises is presented. • This algorithm is applied in Ginzburg–Landau model and two modes laser with Gaussian white noise. • It is proved that this algorithm is scientific. [ABSTRACT FROM AUTHOR]

In this paper, we investigate early warning signals (EWS) of regime shifts in a density-dependent invading population model with time delay, in which the population density is assumed to be disturbed by intrinsic and extrinsic fluctuations. It is shown that the time delay and noises can cause the regime shifts between low and high population density states. The regime shift time (RST) as a function of noise intensity exhibits a maximum, which identifies the signature of the noise-enhanced stability of the low density state, while the time delay weakens the stability of the low density state. Applying the Kramers time technique, we also discuss the intersection point of the RST between low and high population density states, i.e., a critical point in the RST is found. Therefore, the critical point may give an EWS of regime shifts from one alternative state to another one for the changes in the noise parameters and time delay. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the stochastic resonance phenomenon in a vegetation ecological system with time delay, at which the vegetation dynamics is assumed to be disturbed by both intrinsic and extrinsic noises. The signal-to-noise ratio is calculated when a weak periodic signal is added to the system. The impacts of time delay and correlation strength between two noises on the signal-to-noise ratio are discussed, respectively. Our research results show that: (i) the increase of or can enhance the stochastic resonance in the signal-to-noise ratio as a function of intrinsic noise strength ; (ii) on the contrary, the increase of or can weaken the stochastic resonance in the signal-to-noise ratio as a function of extrinsic noise strength ; and (iii) the increase of can lead to double stochastic resonance phenomenon in the signal-to-noise ratio as a function of . [Copyright &y& Elsevier]

We study an inertial Brownian particle moving in a spatially-periodic symmetric potential under the influence of a time periodic and constant biasing driving force, and a Gaussian white noise. Within tailored parameter regimes, our results show: (i) the phenomenon of the absolute negative mobilities (ANMs) in different regimes of the constant bias, with the potential fluctuations that can diminish the ANMs and the vanishing of ANMs for larger potential fluctuations; and (ii) the multiple current reversals as a function of the constant bias, observed for smaller potential fluctuations. • We study an inertial Brownian particle moving in a spatially-periodic symmetric potential. • We show that the phenomenon of the absolute negative mobilities exists. • Multiple current reversals as a function of the constant bias can be observed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamical properties of active Brownian particles (ABPs) in the Schweitzer–Ebeling–Tilch (SET) model with time delay feedback which is driven by external and internal noises. The effects of time delay feedback, external and internal noises on the stationary probability distribution (SPD) and the mean first passage time (MFPT) of the ABPs are discussed, respectively. The results are shown as following: (i) the intensity of time delay feedback (K) can induce the transition between bimodal to unimodal states in the motion of a particle on the SPD, and the time delay can enhance the impacts of the intensity of time delay feedback K inducing transitions from the two stable states (ii) the MFPT as function of the noise strengths shows a maximum, which implies the signature of noise-enhanced stability (NES) phenomenon of the velocity v − in the ABPs for SET model. The positive or negative time delay feedback can enhance or weaken the stability of the motion of the ABPs. • We investigate dynamical properties of ABPs in the SET model. • Time delay can induces transition from two stable states. • MFPT as function of the noise strengths can be observed the maximum. [ABSTRACT FROM AUTHOR]

Ecological dynamic systems often undergo catastrophic regime shifts and have tipping points. Due to the complex interactions and feedbacks among different components of the systems, predicting such transition is a challenging task. This paper investigates the transition patterns of vegetation collapse in semiarid grazing systems. We propose the fractal dimension as a spatial early warning signal to detect this transition. The fractal dimension considers the spatial evolution from the perspective of self-similarity between vegetation. We show that the fractal dimension always decreases to a minimum when the system approaches the critical region, indicating a loss of resilience. We also assess the sensitivity of the fractal dimension under different scenarios of diffusion coefficients and noise levels, which affect the spatial patterns of the vegetation. We compare and analyze the fractal dimension with two commonly used metrics, spatial variance and skewness, and a novel deep learning method in the current research. We also investigate how well the fractal dimension performs with lower-resolution spatial data. Results indicate that the fractal dimension successfully predicts impending critical transition. It turns out that the fractal dimension is a reliable indicator and has significant implications for preventing desertification. • Fractal-based spatial indicator predicts catastrophic regime shifts in ecological systems. • Fractal dimension drops to a minimum, a reliable warning signal for critical transitions. • Fractal dimension outperforms two generic indicators and deep learning. • The study advances spatial early warning signals, offers monitoring tool. [ABSTRACT FROM AUTHOR]

Abstract Considering additive and multiplicative periodic signals, we have investigated the stochastic resonance (SR)phenomenon in an insect ecosystem with two different types of time delays, at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises. The signal-to-noise ratio (SNR) is calculated when two different weak periodic signals are added to the insect system. It is shown from the SNR that the additive and multiplicative periodic signals can cause the SR and double SR in the case of time delays in the stochastic and deterministic force, respectively. A detailed study of the SNR depending on various noise characteristics is performed, and the main results about SR are compared for two different cases of time delays. Highlights • We have investigated stochastic resonance (SR) phenomenon in an insect ecosystem. • Additive and multiplicative periodic signals can cause the SR and double SR. • Detailed study of the SNR depending on various noise characteristics is performed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the role of correlated multiplicative ( κ 1 ) and additive ( κ 2 ) noises in a modified energy conversion depot model, at which it is added a linear term in the conversion of internal energy of active Brownian particles (ABPs). The linear term ( a 1 ≠ 0 . 0 ) in energy conversion model breaks the symmetry of the potential to generate motion of the ABPs with a net transport velocity. Adopt a nonlinear Langevin approach, the transport properties of the ABPs have been discussed, and our results show that: (i) the transport velocity 〈 υ 1 〉 of the ABPs are always positive whether the correlation intensity λ = 0 . 0 or not; (ii) for a small value of the multiplicative noise intensity κ 1 , the variation of 〈 υ 1 〉 with λ shows a minimum, there exists an optimal value of the correlation intensity λ at which the 〈 υ 1 〉 of the ABPs is minimized. But for a large value of κ 1 , the 〈 υ 1 〉 monotonically decreases; (iii) the transport velocity 〈 υ 1 〉 increases with the increase of the κ 1 or κ 2 , i.e., the multiplicative or additive noise can facilitate the transport of the ABPs; and (iv) the effective diffusion increases with the increase of a 1 , namely, the linear term in modified energy conversion model of the ABPs can enhance the diffusion of the ABPs. [ABSTRACT FROM AUTHOR]

Based on the kinetic model for obtaining emergent bistability proposed by Tan et al. (2009), the effects of the fluctuations of protein synthesis rate and maximum dilution rate, the cross-correlation between two noises, and the time delay and the strength of the feedback loop in the synthetic gene circuit have been investigated through theoretical analysis and numerical simulation. Our results show that: (i) the fluctuations of protein synthesis rate and maximum dilution rate enhance the emergent bimodality of the probability distribution phenomenon, while the cross-correlation between two noises( λ ), the time delay( τ ) and the strength of the feedback loop( K ) cause it to disappear; and (ii) the mean first passage time(MFPT) as functions of the noise strengths exhibits a maximum, this maximum is called noise-delayed switching (NDS) of the high concentration state. The NDS phenomenon shows that the noise can modify the stability of a metastable system in a counterintuitive way, the system remains in the metastable state for a longer time compared to the deterministic case. And the τ and the K enhances the stability of the ON state. The physical mechanisms for the switch between the ON and OFF states can be explained from the point of view of the effective potential. [ABSTRACT FROM AUTHOR]

In this article we mainly focus on the temporal correlation between the past dynamic fluctuations and the future motion of the dynamic variables in the climate system by means of a new temporal correlation function. When the complex climate system is assumed to be in the stationary states, that is, the dynamic effects of the non-stationary states are not considered, the above correlation is weak or even non-existent. Unexpectedly, a good correlation is shown when the dynamic effects of the non-stationary states are taken into account. Subsequently, we analyze the main factors contributing to these results and conclude that the small fluctuations make a major contribution to this. At the same time, we also find that this correlation function is somewhat stable over time scales. Finally, we extend our analysis by using the persistence probabilities. Knowing these is of key importance for the study of climate analysis and prediction. • Our research object is the daily data of climate indicators for four typical cities in southwest China. • We find this temporal correlation to be more pronounced for some indicators in our study. • Our findings may contribute to the study of climate analysis and prediction. [ABSTRACT FROM AUTHOR]

The generation of heat flux and its controlled manipulation are old yet important problems. In this paper, we investigate heat flux across deformable Frenkel–Kontorova lattices tuned by the time-varying heat bath. We considered two different cases separately. For the smooth case, we found that for time-varying heat bath driven by different frequencies, suitable shape parameters can control the magnitude and even the direction of the heat flux. We further analyze the influence of the time-varying heat bath (including driving amplitude, phase shift and reference temperature) on the heat flux and find that the driving amplitude can greatly increase the magnitude of the heat flux. For the roughness case, the results suggest that the roughness can weaken the reversal of heat flux or even eliminate this phenomenon. Moreover, for relatively large roughness, the heat flux is close to zero. Our research results reveal the effect of time-varying heat bath and deformable potential energy on heat flux and can be a reference for the study of the nonlinear response mechanism of low-dimensional materials and the application of heat flux controllers. • We investigate heat flux across deformable FK lattices tuned by the time-varying heat bath. • For the roughness case, the roughness can weaken the reversal of heat flux or even eliminate it. • For relatively large roughness, the heat flux is close to zero. [ABSTRACT FROM AUTHOR]

In this paper, the protein switch in a single-gene network with time delays is investigated, where the gene expression is assumed to be disturbed by multiplicative and additive noises. The impacts of time delays τ d and τ s in degradation and synthesis processes, time delay τ g in global process and cross-correlation between two noises ( λ i , and i = d , s , g ) on the probability distribution and switch time (ST) from low protein level (OFF state) to high one (ON state) are discussed, respectively. Our results show that (1) the increase of the cross-correlation between two noises ( λ i ) can induce protein switches from ON state to OFF one; (2) for λ i ⩾ 0 , the increase of τ d can induce protein switches from OFF state to ON one, while τ s (or τ g ) can induce protein switches from the ON state to the OFF one, but for λ i < 0 , the τ d (or τ s ) can induce protein switches from the OFF state to the ON one, while τ g can induce protein switches from the ON state to the OFF one; (3) the ST as functions of the noise intensities exhibits a maximum, which is the signature of the noise enhanced stability (NES) of the OFF state, while the increase of τ d can cause the NES phenomenon to disappear; and (4) τ d and τ s play opposing roles in the ST, i.e., the impacts of the time delays τ d and τ s on ST can be canceled each other out. [ABSTRACT FROM AUTHOR]

We investigate the transport properties of active Brownian particle (ABP) in the Schweitzer–Ebeling–Tilch (SET) model, driven by cross-correlation between multiplicative and additive noises and a bias force. It is shown that (i) the cross-correlated noises and bias force can lead to a transition from bimodal to unimodal, and the numerical simulations are in good agreement with the theoretical results; (ii) the cross-correlated noises and bias force can enhance the transport and weaken the diffusion of the ABP; (iii) the multiplicative noise can facilitate the transport and enhance the diffusion of the ABP, and a giant diffusion by a larger multiplicative noise, whereas the additive noise can weaken the transport of the ABP. A physical mechanism for the transport and diffusion of the ABP is derived from the effective velocity potential for the above findings; and (iv) the cross-correlated noises and bias force can enhance the collective motion of coupled active Brownian particles (ABPs), i.e., better synchronization between N coupled ABPs. It can provide a possible strategy for controlling active motion. • Cross-correlated noise and bias force can lead to a transition from bimodal to unimodal. • Cross-correlated noises and bias force can enhance the transport and weaken the diffusion of the ABP. • Multiplicative noise can facilitate transport and enhance diffusion of the ABP, whereas the additive noise can weaken the transport of the ABP. • Cross-correlated noises and bias force can enhance the collective motion of coupled ABPs. [ABSTRACT FROM AUTHOR]