The Investigation Of Anomalous Transports And Control Mechanisms In Nonlinear Stochastic Dynamical Systems

Of great significance is the theory of the Brownian motion that is intensively used in physics,chemistry,biology,medicine,economy,ecology,material science,etc.It,therefore,has been in the research spotlight for more than 100 years.For the particles moving in the systems far from equilibrium,there exists the occurrence of paradoxical situations since the laws of thermodynamics no longer possess validity.Recently,the anomalous transport in various nonlinear stochastic dynamical systems has been extensively studied.However,the underlying dynamical mechanism of these phenomena is not clear.It is well known that Chaos is ubiquitous in nonlinear systems and very sensitive to the initial conditions and system parameters.The relationship between anomalous transport and chaotic dynamics is not clear.Therefore,our motivation is to explore whether the anomalous transport of particles in nonlinear stochastic dynamical systems is related to chaotic dynamics or not,and what is the underlying dynamical mechanism behind anomalous transport.Based on dynamical mechanisms,we reveal the working principle of particle devices via control transport.The main results are as follows:1.We study the anomalous transports and their dynamical mechanisms of a particle moving in a nonlinear dynamical system.We find that the varying friction coefficient lead to the absolute negative mobility,differential negative mobility,and giant positive mobility.The fluctuation of friction coefficient enhances or weakens these transports,even eliminates them.We discuss the underlying dynamical mechanism through the basins of attraction,the probability distribution of velocity,and diffusion.We also find that for suitable parameters,the existence of certain appropriate friction coefficients can enhance the transport of the particle,which may be interpreted as the negative friction coefficient.For the small fluctuation,there coexists anomalous transport and anomalous diffusion,whereas all of them vanish for the large fluctuation.Our findings may extensively exist in the transport for the surface of materials.2.We here investigate the anomalous transport of a particle moving in a nonlinear chaotic dynamical system with a stochastic resetting and a rough potential,and focus on how the stochastic resetting,roughness,and noise affect the transports of the particle.We uncover the dynamical mechanism for stochastic resetting resulting in the anomalous transport in a nonlinear chaotic system:The particle is reset to a new basin of attraction which may be different from the initial basin of attraction from the view of dynamics.From the view of the energy landscape,the particle is reset to a new energy state of the energy landscape which may be different from the initial energy state.The roughness and noise also lead to anomalous transport.The combination of the stochastic resetting,roughness,and noise can enhance the transport and tune negative mobility,the enhanced stability of the system,and the resonant-like activity.We analyze these results through variances and correlation functions.Our results can be extensively applied in the biology,physics,and chemistry,even social system.3.We numerically investigate negative mobility and chaotic dynamics of a particle moving in a periodic double-well substrate potential.The deterministic model shows that the varying shape parameter and driving forces can cause negative mobility,differential negative mobility,and giant positive mobility through the average velocity.We analyze these findings via the bifurcation diagram,maximal Lyapunov exponent,time series,phase-space map,and the power spectrum,and find that strong chaotic attractors(SCAs)can give rise to negative mobility.We propose an underlying mechanism that SCAs can result in the negative mobility.The stochastic model shows that the noise intensity can enhance or result in negative and positive mobilities,whereas correlation time can enhance,or weaken,even eliminate them.Our findings may be potentially useful for research on anomalous transports of the particles and on designs of various devices,such as atomic chains,crystals with dislocations,and superconducting nanowires,etc.4.We numerically investigate the rectification of the probability flux and dynamical relaxation of particles moving in an out-of-equilibrium system consisting of two substrate potentials.The deterministic model exhibits the perfect rectification of the probability flux,ratchet effect,and the dependence of the unpredictability of the dynamics on basin of attraction for random initial states.In contrast,the stochastic model displays that the rectification is sensitive to the temperature and an external bias.They can induce kinetic phase transitions between no transport and a finite net transport.These transitions lead to an unexpected phenomenon,called negative rectification.The results are analyzed through the corresponding time-dependent diffusion coefficient,information entropy(IE),etc.At a low temperature,anomalous diffusions occur in system.For the occurrence of the flux in certain parameter regimes,the larger the diffusion is,the smaller the corresponding IE is,and vice versa.We also present the selected parameter regimes for the emergence of the rectification and negative rectification.Our work provides not only a way of the rectification for the transport of various particles(e.g.,ion,electron,photon,phonon,molecular,DNA chain,nanoswimmer,dust particle,etc)in physics,chemistry,biology,and material science,but also a design of various circuits.5.We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles.Via the power spectrum density of a single particle,we find that there exists a nontrivial resonance.For interacting particles,we find that the interaction between the probe particle and other particles can lead to the resonance,too.Thus we propose the system with the Brownian particle as a probe,which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system.The probe is potentially useful for detecting microscopic and nanometer-scale particles.Overall,we numerically study the anomalous transport of inertial particles and its dynamics(chaos and basin of attraction)in nonlinear stochastic dynamical systems,and reveal the dynamical mechanism of anomalous transport.Based on the mechanism,we tune the rectification in system consisting of the two substrate potential,and present the working principle of the negative rectification for the diode of inertial particle.Additionally,we also investigate the resonance of the underdamped scaled Brownian motion in the bistable system,and reveal the working principle for the probe of inertial Brownian particle.