Gene transcriptional regulation （TR） processes are often described by coupled nonlinear ordinary differential equations （ODEs）. When the dimension of TR circuits is high （e.g. n≥3） the motions of the correspond...Gene transcriptional regulation （TR） processes are often described by coupled nonlinear ordinary differential equations （ODEs）. When the dimension of TR circuits is high （e.g. n≥3） the motions of the corresponding ODEs may, very probably, show self-sustained oscillations and chaos. On the other hand, chaoticity may be harmful for the normal biological functions of TR processes. In this letter we numerically study the dynamics of 3-gene TR ODEs in great detail, and investigate many 4-, 5-, and lO-gene TR systems by randomly choosing figures and parameters in the conventionally accepted ranges. And we find that oscillations are very seldom and no chaotic motion is observed, even if the dimension of systems is sufficiently high （n≥3）. It is argued that the observation of nonchaoticity of these ODEs agrees with normal functions of actual TR processes.展开更多
Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is ...Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.展开更多
In this paper,we investigate the existence of strange nonchaotic attractors(SNAs)in a slender rigid rocking block under quasi-periodic forcing with two frequencies.We find that an SNA can exist between a quasi-periodi...In this paper,we investigate the existence of strange nonchaotic attractors(SNAs)in a slender rigid rocking block under quasi-periodic forcing with two frequencies.We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor,or between two chaotic attractors.In particular,we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors.This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems.The properties of SNAs are verified by the Lyapunov exponent,rational approximation,phase sensitivity,power spectrum,and separation of nearby trajectories.展开更多
The basis weight control loop of the papermaking process is a non-linear system with time-delay and time-varying.It is impractical to identify a model that can restore the model of real papermaking process.Determining...The basis weight control loop of the papermaking process is a non-linear system with time-delay and time-varying.It is impractical to identify a model that can restore the model of real papermaking process.Determining a more accurate identification model is very important for designing the controller of the control system and maintaining the stable operation of the papermaking process.In this study,a strange nonchaotic particle swarm optimization(SNPSO)algorithm is proposed to identify the models of real papermaking processes,and this identification ability is significantly enhanced compared with particle swarm optimization(PSO).First,random particles are initialized by strange nonchaotic sequences to obtain high-quality solutions.Furthermore,the weight of linear attenuation is replaced by strange nonchaotic sequence and the time-varying acceleration coefficients and a mutation rule with strange nonchaotic characteristics are utilized in SNPSO.The above strategies effectively improve the global and local search ability of particles and the ability to escape from local optimization.To illustrate the effectiveness of SNPSO,step response data are used to identify the models of real industrial processes.Compared with classical PSO,PSO with timevarying acceleration coefficients(PSO-TVAC)and modified particle swarm optimization(MPSO),the simulation results demonstrate that SNPSO has stronger identification ability,faster convergence speed,and better robustness.展开更多
基金National Natural Science Foundation of China under Grant Nos.10335010 and 70431002the Nonlinear Science 973 Project under Grant No.10675020
文摘Gene transcriptional regulation （TR） processes are often described by coupled nonlinear ordinary differential equations （ODEs）. When the dimension of TR circuits is high （e.g. n≥3） the motions of the corresponding ODEs may, very probably, show self-sustained oscillations and chaos. On the other hand, chaoticity may be harmful for the normal biological functions of TR processes. In this letter we numerically study the dynamics of 3-gene TR ODEs in great detail, and investigate many 4-, 5-, and lO-gene TR systems by randomly choosing figures and parameters in the conventionally accepted ranges. And we find that oscillations are very seldom and no chaotic motion is observed, even if the dimension of systems is sufficiently high （n≥3）. It is argued that the observation of nonchaoticity of these ODEs agrees with normal functions of actual TR processes.
基金Project supported by the National Natural Science Foundation of China （Grant No 59577025） and the Fundamental Research Foundation of Tsinghua University （Grant No JC2001021）. The authors would like to thank Professor Tang Tongyi for much beneficial help.
文摘Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.
基金supported by the National Natural Science Foundation of China under grant number 11971019.
文摘In this paper,we investigate the existence of strange nonchaotic attractors(SNAs)in a slender rigid rocking block under quasi-periodic forcing with two frequencies.We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor,or between two chaotic attractors.In particular,we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors.This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems.The properties of SNAs are verified by the Lyapunov exponent,rational approximation,phase sensitivity,power spectrum,and separation of nearby trajectories.
基金support received from the National Natural Science Foundation of China(Grant No.62073206)Technical Innovation Guidance Project of Shaanxi Province(Grant No.2020CGHJ-007).
文摘The basis weight control loop of the papermaking process is a non-linear system with time-delay and time-varying.It is impractical to identify a model that can restore the model of real papermaking process.Determining a more accurate identification model is very important for designing the controller of the control system and maintaining the stable operation of the papermaking process.In this study,a strange nonchaotic particle swarm optimization(SNPSO)algorithm is proposed to identify the models of real papermaking processes,and this identification ability is significantly enhanced compared with particle swarm optimization(PSO).First,random particles are initialized by strange nonchaotic sequences to obtain high-quality solutions.Furthermore,the weight of linear attenuation is replaced by strange nonchaotic sequence and the time-varying acceleration coefficients and a mutation rule with strange nonchaotic characteristics are utilized in SNPSO.The above strategies effectively improve the global and local search ability of particles and the ability to escape from local optimization.To illustrate the effectiveness of SNPSO,step response data are used to identify the models of real industrial processes.Compared with classical PSO,PSO with timevarying acceleration coefficients(PSO-TVAC)and modified particle swarm optimization(MPSO),the simulation results demonstrate that SNPSO has stronger identification ability,faster convergence speed,and better robustness.
