A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the genera...A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the generation of high-frequency quasi-mode due to nonlinear coupling of two RSAEs,which is then damped due to coupling with the shear Alfvén continuum,and leads to the nonlinear saturation of the primary RSAEs.An estimation of the nonlinear damping rate is also provided.展开更多
This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservatio...This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.展开更多
It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable sys...It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.展开更多
A special integrable nonlocal nonlinear Schroodinger equation, NNLS, or namely Alice-Bob NLS（ABNLS）equation is investigated. By means of the general N-th Darboux transformation, one can get various interesting solut...A special integrable nonlocal nonlinear Schroodinger equation, NNLS, or namely Alice-Bob NLS（ABNLS）equation is investigated. By means of the general N-th Darboux transformation, one can get various interesting solutions to display different types of structures especially for solitons. By using the Darboux transformation, its soliton solutions are obtained. Finally, by adjusting the values of free parameters, different kinds of solutions such as kinks, complexitons and rogue-wave solutions are explicitly exhibited. It is found that these solutions are quite different from the ones of the classical NLS equation.展开更多
By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations, the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travellin...By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations, the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travelling wave solutions is studied and the bifurcation parametric sets are shown. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained.展开更多
The modified flat-bottom potential(MFBP)is given by the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviour of the effective quark-gluon coupling.Theπmes...The modified flat-bottom potential(MFBP)is given by the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviour of the effective quark-gluon coupling.Theπmeson electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson equation and Bethe-Salpeter equation in simplified impulse approximation(dressed vertex)with MFBP.All our numerical results give good fit to experimental values.展开更多
We calculate the energy level shift of a static ground state two-level atom interacting with fluctuating massless scalar fields in the Hartle–Hawking vacuum outside a Schwarzschild black hole.It is found that the ene...We calculate the energy level shift of a static ground state two-level atom interacting with fluctuating massless scalar fields in the Hartle–Hawking vacuum outside a Schwarzschild black hole.It is found that the energy level shift is position-dependent and gives rise to a force on the atom besides the classical gravitational force.This force behaves like r^(-1)(r-2M)^(-1) for r approaching 2M,whereas it behaves like r^(-2) for large r.展开更多
The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require...The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.展开更多
In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The revers...In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The reversed shear Alfvén eigenmode(RSAE)as a unique branch of the shear Alfvén wave in this equilibrium,can exist with a broad spectrum in wavenumber and frequency,and be resonantly driven unstable by energetic particles(EP).After briefly discussing the RSAE linear properties in burning plasma condition,we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels,and illustrate their potentially important role in reactor-scale fusion plasmas.By means of simplified hybrid MHD-kinetic simulations,the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP,as results of weak/vanishing magnetic shear and relatively low frequency.Through the route of wave-EP nonlinearity,the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure,and the resultant EP transport generally has a convective feature.The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations.Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory,and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE.Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode,which may effectively transfer the EP energy to fuel ions via collisionless Landau damping.Moreover,zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope,and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.展开更多
This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardi...This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardin et al 2012 J.Comput.Sci.Discovery 6014002).Using an HL-2A-like equilibrium,we confirm that in the linear phase,the impact of REs on resistive internal kink instabilities is consistent with previous research.In the nonlinear phase,as the runaway current fully replaces the plasmas current,we observe a significant suppression of sawtooth oscillations,with the first sawtooth cycle occurring earlier compared to the case without runaway current.Following the first sawtooth collapse,plasma current density,runaway current density,and safety factor(q)flatten within the q=1 surface,albeit displaying fine structures.Subsequently,the growing high torodial(n)and poloidal(m)mode number modes disrupt the magnetic surfaces,leading to the loss of REs outside the q=1 surface,while minimally affecting the majority of REs well-confined within it.Thus,in the current model,the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current,as REs are assumed to be collisionless.In addition,the final profile of runaway current density exhibits increased steepening near the q=1 surface in contrast to the initial profile,displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the n=0 component.Finally,detailed convergence tests are conducted to validate the numerical simulations.展开更多
For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; ...For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.展开更多
The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation. A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form. The super mKdV system is changed...The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation. A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form. The super mKdV system is changed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV(BSmKdV)equation admits Painlevé property by the standard singularity analysis. The traveling wave solutions of the BSmKdV system are presented by the mapping and deformation method. We also provide other ideas to construct new super integrable systems.展开更多
This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors.The two networks can be undirected or directed,and they may also cont...This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors.The two networks can be undirected or directed,and they may also contain isolated nodes and clusters.By using suitable controllers,sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory.Finally,numerical examples are examined to illustrate the effectiveness of the analytical results.The effect of control parameters on the synchronization time is also numerically demonstrated.展开更多
This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochast...This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.展开更多
The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for...The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained.展开更多
We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-...We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-adaptive mechanism correctly represents essential characteristics of self-adaptation in complex systems. We also show that this method is reasonable both from the coupling viewpoint in physics and from the controller design viewpoint in control theory.展开更多
We study the Alice-Bob peakon system generated from an integrable peakon system using the strategy of the so- called Alice-Bob non-local KdV approach [Scientific Reports 7 （2017） 869]. Nonlocal integrable peakon equ...We study the Alice-Bob peakon system generated from an integrable peakon system using the strategy of the so- called Alice-Bob non-local KdV approach [Scientific Reports 7 （2017） 869]. Nonlocal integrable peakon equations are obtained and shown to have peakon solutions.展开更多
By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means tha...By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means that our method enables this three_dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.展开更多
A truncation for the Laurent series in the Padnleve analysis of the KdV equation is restudied. When the truncation occurs the singular manifold satisfies two compatible fourth-order PDEs, which are homogeneous of degr...A truncation for the Laurent series in the Padnleve analysis of the KdV equation is restudied. When the truncation occurs the singular manifold satisfies two compatible fourth-order PDEs, which are homogeneous of degree 3. Both of the PDEs can be factored in the operator sense. The common factor is a third-order PDE, which is homogeneous of degree 2. The first few Invariant manifolds of the third-order PDE are studied. We find that the invariant manifolds of the third-order PDE can be obtained by factoring the invariant manifolds of the KdV equation. A numerical solution of the third-order PDE facts about the third-order PDE. is also presented. The solution reveals some interesting展开更多
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDB0790000)the Collaborative Innovation Program of Hefei Science Center,CAS(No.2022HSC-CIP008)National Natural Science Foundation of China(Nos.12275236 and 12261131622)。
文摘A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the generation of high-frequency quasi-mode due to nonlinear coupling of two RSAEs,which is then damped due to coupling with the shear Alfvén continuum,and leads to the nonlinear saturation of the primary RSAEs.An estimation of the nonlinear damping rate is also provided.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029+1 种基金the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001 the Doctoral Foundation of Binzhou University under Grant No.2009Y01
文摘This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.
基金Supported by National Natural Science Foundation of China under Grant No.10735030Natural Science Foundation of Zhejiang Province under Grant Nos.R609077,Y6090592National Science Foundation of Ningbo City under Grant Nos.2009B21003,2010A610103, 2010A610095
文摘It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.
基金Supported by National Natural Science Foundation of China under Grant No.11435005Ningbo Natural Science Foundation under Grant No.2015A610159+1 种基金Granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502Sponsored by K.C.Wong Magna Fund in Ningbo University
文摘A special integrable nonlocal nonlinear Schroodinger equation, NNLS, or namely Alice-Bob NLS（ABNLS）equation is investigated. By means of the general N-th Darboux transformation, one can get various interesting solutions to display different types of structures especially for solitons. By using the Darboux transformation, its soliton solutions are obtained. Finally, by adjusting the values of free parameters, different kinds of solutions such as kinks, complexitons and rogue-wave solutions are explicitly exhibited. It is found that these solutions are quite different from the ones of the classical NLS equation.
文摘By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations, the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travelling wave solutions is studied and the bifurcation parametric sets are shown. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained.
基金Supported by the National Natural Science Foundation of China under Grant No.19875048.
文摘The modified flat-bottom potential(MFBP)is given by the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviour of the effective quark-gluon coupling.Theπmeson electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson equation and Bethe-Salpeter equation in simplified impulse approximation(dressed vertex)with MFBP.All our numerical results give good fit to experimental values.
基金Supported in part by the National Natural Science Foundation of China under Grants Nos 11075083,11005038 and 10935013the Zhejiang Provincial Natural Science Foundation of China under Grant No Z6100077+2 种基金the National Basic Research Program of China under Grant No 2010CB832803the PCSIRT under Grant No IRT0964the Hunan Provincial Natural Science Foundation of China under Grant No 11JJ7001.
文摘We calculate the energy level shift of a static ground state two-level atom interacting with fluctuating massless scalar fields in the Hartle–Hawking vacuum outside a Schwarzschild black hole.It is found that the energy level shift is position-dependent and gives rise to a force on the atom besides the classical gravitational force.This force behaves like r^(-1)(r-2M)^(-1) for r approaching 2M,whereas it behaves like r^(-2) for large r.
基金supported by the National Key R&D Program of China(No.2017YFE0301900)National Natural Science Foundation of China(No.11875233)Users of Excellence Program of Hefei Science Center CAS(No.2021HSC-UE016)。
文摘The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.
基金supported by National Natural Science Foundation of China (Nos. 12205251, 12275236 and 12261131622)Italian Ministry for Foreign Affairs and International Cooperation Project (No. CN23GR02)+2 种基金the National Key Research and Development Program of China (Nos. 2019YFE03020003 and 2017YFE0301900)Users of Excellence program of Hefei Science Center CAS (No. 2021HSC-UE016)funded by the European Union via the Euratom Research and Training Programme (No. 101052200–EUROfusion)
文摘In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The reversed shear Alfvén eigenmode(RSAE)as a unique branch of the shear Alfvén wave in this equilibrium,can exist with a broad spectrum in wavenumber and frequency,and be resonantly driven unstable by energetic particles(EP).After briefly discussing the RSAE linear properties in burning plasma condition,we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels,and illustrate their potentially important role in reactor-scale fusion plasmas.By means of simplified hybrid MHD-kinetic simulations,the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP,as results of weak/vanishing magnetic shear and relatively low frequency.Through the route of wave-EP nonlinearity,the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure,and the resultant EP transport generally has a convective feature.The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations.Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory,and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE.Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode,which may effectively transfer the EP energy to fuel ions via collisionless Landau damping.Moreover,zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope,and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.
基金supported in part by the National Key R&D Program of China (No.2022YFE03040002)the Natural Science Foundation of Sichuan (No.2022NSFSC1814)+3 种基金National Natural Science Foundation of China (Nos.12305246,12175053 and 12261131622)the Italian Ministry of Foreign Affairs (No.CN23GR02)the Fundamental Research Funds for the Central Universitiessupported by US Department of Energy (No.DE-AC0209CH11466)。
文摘This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardin et al 2012 J.Comput.Sci.Discovery 6014002).Using an HL-2A-like equilibrium,we confirm that in the linear phase,the impact of REs on resistive internal kink instabilities is consistent with previous research.In the nonlinear phase,as the runaway current fully replaces the plasmas current,we observe a significant suppression of sawtooth oscillations,with the first sawtooth cycle occurring earlier compared to the case without runaway current.Following the first sawtooth collapse,plasma current density,runaway current density,and safety factor(q)flatten within the q=1 surface,albeit displaying fine structures.Subsequently,the growing high torodial(n)and poloidal(m)mode number modes disrupt the magnetic surfaces,leading to the loss of REs outside the q=1 surface,while minimally affecting the majority of REs well-confined within it.Thus,in the current model,the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current,as REs are assumed to be collisionless.In addition,the final profile of runaway current density exhibits increased steepening near the q=1 surface in contrast to the initial profile,displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the n=0 component.Finally,detailed convergence tests are conducted to validate the numerical simulations.
文摘For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11775146,11435005,and 11472177Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213K.C.Wong Magna Fund in Ningbo University
文摘The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation. A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form. The super mKdV system is changed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV(BSmKdV)equation admits Painlevé property by the standard singularity analysis. The traveling wave solutions of the BSmKdV system are presented by the mapping and deformation method. We also provide other ideas to construct new super integrable systems.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61203304,61203055 and 10901145the Fundamental Research Funds for the Central Universities under Grant Nos.2011QNA26,2010LKSX04,and 2010LKSX01
文摘This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors.The two networks can be undirected or directed,and they may also contain isolated nodes and clusters.By using suitable controllers,sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory.Finally,numerical examples are examined to illustrate the effectiveness of the analytical results.The effect of control parameters on the synchronization time is also numerically demonstrated.
基金supported by the National Natural Science Foundation of China (Grant No. 10901145)
文摘This paper investigates the chaotic synchronization between the noise-perturbed Lorenz system and one of the noise-perturbed Chen and Lii systems. Based on the active control method and the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived. Numerical simulations are also shown to demonstrate the effectiveness of these theoretic results.
基金Supported by the Global Change Research Program China under Grant No.2015CB953904the National Natural Science Foundations of China under Grant Nos.11435005,11175092,and 11205092+1 种基金Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213K.C.Wong Magna Fund in Ningbo University
文摘The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10372054 and 70431002.
文摘We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-adaptive mechanism correctly represents essential characteristics of self-adaptation in complex systems. We also show that this method is reasonable both from the coupling viewpoint in physics and from the controller design viewpoint in control theory.
基金Supported by the Global Change Research Program of China under Grant No 2015CB953904the National Natural Science Foundation of China under Grant No 11435005+3 种基金the Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No ZF1213the K.C.Wong Magna Fund at Ningbo Universitythe UTRGV President's Endowed Professorshipthe Seed Grant of the UTRGV College of Science
文摘We study the Alice-Bob peakon system generated from an integrable peakon system using the strategy of the so- called Alice-Bob non-local KdV approach [Scientific Reports 7 （2017） 869]. Nonlocal integrable peakon equations are obtained and shown to have peakon solutions.
文摘By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means that our method enables this three_dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.
基金Supported in part by the National Natural Science Foundation of China under Grant No 90503006, and Ningbo Natural Science Foundation under Grant No 2006A610093.
文摘A truncation for the Laurent series in the Padnleve analysis of the KdV equation is restudied. When the truncation occurs the singular manifold satisfies two compatible fourth-order PDEs, which are homogeneous of degree 3. Both of the PDEs can be factored in the operator sense. The common factor is a third-order PDE, which is homogeneous of degree 2. The first few Invariant manifolds of the third-order PDE are studied. We find that the invariant manifolds of the third-order PDE can be obtained by factoring the invariant manifolds of the KdV equation. A numerical solution of the third-order PDE facts about the third-order PDE. is also presented. The solution reveals some interesting
