In ecological environments,the survival environment of species is often inhomogeneous,and the reproductive process is affected by time delay.System with nonlocal effects and delay can more accurately simulate changes ...In ecological environments,the survival environment of species is often inhomogeneous,and the reproductive process is affected by time delay.System with nonlocal effects and delay can more accurately simulate changes in population density.In this paper,we consider a reaction-diffusion-advection model with nonlocal delay and Dirichlet boundary conditions.First of all,we investigate the well-posedness of solution of model.Then,the existence of positive steady state is proofed by implicit function theorem.Based on a priori estimate for the eigenvalue,we prove the stability of the positive steady state and conclude the associated distribution of Hopf bifurcation.Our research indicates that the combined effects of nonlocal and time delays have a certain impact on the dynamics of the model.展开更多
Control over charge transport in molecular–scale devices requires a deep understanding of how minute structural changes influence electronic properties.Here,we demonstrate dual transport regimes in tunnel junctions o...Control over charge transport in molecular–scale devices requires a deep understanding of how minute structural changes influence electronic properties.Here,we demonstrate dual transport regimes in tunnel junctions of n-alk-1-yne(CnA)molecules with gold electrodes driven by conformational bifurcation—the emergence of two nearly isoenergetic(planar and skewed)molecular conformers(dihedral anglesα=180°andα≈65°at the alkyne terminus in the gas phase).Although the energy differences are small,these subtle conformational differences manifest as distinct transport behaviors,uncovered through unsupervised machine learning,which identified two junction groups:“short”and“long”chains,with distinct attenuation factors(β_(short)≈1.0 vs.β_(long)≈0.74)and contact conductances(G_(c,short)≈200μS vs.G_(c,long)≈8μS).This dramatic impact of the dihedral angle exceeds the impact of the inter-ring twist angle in biphenyl-based junctions and rivals changes induced by switching from gold to platinum electrodes or from monothiol to dithiol anchors in oligoacene and oligophenylene junctions.X-ray photoelectron spectroscopy(XPS)confirmed this bifurcation,linking the“short”and“long”groups to planar and skewed conformers,with dihedrals remarkably agreeing with the gas-phase values.This work establishes conformational bifurcation as a promising route for designing programmable nanotransport properties through anchor-group control.展开更多
This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural condit...This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).展开更多
One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite...One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.展开更多
We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portrai...We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.展开更多
This study investigates the bifurcation dynamics underlying rhythmic transitions in a biophysical hippocampal–cortical neural network model.We specifically focus on the membrane potential dynamics of excitatory neuro...This study investigates the bifurcation dynamics underlying rhythmic transitions in a biophysical hippocampal–cortical neural network model.We specifically focus on the membrane potential dynamics of excitatory neurons in the hippocampal CA3 region and examine how strong coupling parameters modulate memory consolidation processes.Employing bifurcation analysis,we systematically characterize the model's complex dynamical behaviors.Subsequently,a characteristic waveform recognition algorithm enables precise feature extraction and automated detection of hippocampal sharp-wave ripples(SWRs).Our results demonstrate that neuronal rhythms exhibit a propensity for abrupt transitions near bifurcation points,facilitating the emergence of SWRs.Critically,temporal rhythmic analysis reveals that the occurrence of a bifurcation is not always sufficient for SWR formation.By integrating one-parameter bifurcation analysis with extremum analysis,we demonstrate that large-amplitude membrane potential oscillations near bifurcation points are highly conducive to SWR generation.This research elucidates the mechanistic link between changes in neuronal self-connection parameters and the evolution of rhythmic characteristics,providing deeper insights into the role of dynamical behavior in memory consolidation.展开更多
In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact ...In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution （xs（t）, O, zs（t）） is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period T the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.展开更多
This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theo...This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.展开更多
As a typical biochemical reaction, the process of continuous fermentation of ethanol is studied in this paper. An improved model is set forward and in agreement with experiments. Nonlinear oscillations of the process ...As a typical biochemical reaction, the process of continuous fermentation of ethanol is studied in this paper. An improved model is set forward and in agreement with experiments. Nonlinear oscillations of the process are analyzed with analytical and numerical methods. The Hopf bifurcation region is fixed and further analyses are given.展开更多
The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is stu...The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.展开更多
基金Supported by the Natural Science Foundation of Shanghai(23ZR1401700)National Natural Science Foundation of China(12471157)。
文摘In ecological environments,the survival environment of species is often inhomogeneous,and the reproductive process is affected by time delay.System with nonlocal effects and delay can more accurately simulate changes in population density.In this paper,we consider a reaction-diffusion-advection model with nonlocal delay and Dirichlet boundary conditions.First of all,we investigate the well-posedness of solution of model.Then,the existence of positive steady state is proofed by implicit function theorem.Based on a priori estimate for the eigenvalue,we prove the stability of the positive steady state and conclude the associated distribution of Hopf bifurcation.Our research indicates that the combined effects of nonlocal and time delays have a certain impact on the dynamics of the model.
基金financial support from the National Key R&D Program of China(2023YFA1407100)the National Natural Science Foundation of China(22373026)+1 种基金Guangdong Science and Technology Department(2021B0301030005,STKJ2023072,GDZX2304005,GDZX2504001,and 2021QN02X538)Ioan Bâldea gratefully acknowledges computational support by the state of Baden-Württemberg through bwHPC and the German Research Foundation through Grant Nos.INST 40/575-1,35/1597-1,and 35/1134-1(JUSTUS 2,bwUniCluster 2/3,and bwForCluster/MLS&WISO/HELIX 2).
文摘Control over charge transport in molecular–scale devices requires a deep understanding of how minute structural changes influence electronic properties.Here,we demonstrate dual transport regimes in tunnel junctions of n-alk-1-yne(CnA)molecules with gold electrodes driven by conformational bifurcation—the emergence of two nearly isoenergetic(planar and skewed)molecular conformers(dihedral anglesα=180°andα≈65°at the alkyne terminus in the gas phase).Although the energy differences are small,these subtle conformational differences manifest as distinct transport behaviors,uncovered through unsupervised machine learning,which identified two junction groups:“short”and“long”chains,with distinct attenuation factors(β_(short)≈1.0 vs.β_(long)≈0.74)and contact conductances(G_(c,short)≈200μS vs.G_(c,long)≈8μS).This dramatic impact of the dihedral angle exceeds the impact of the inter-ring twist angle in biphenyl-based junctions and rivals changes induced by switching from gold to platinum electrodes or from monothiol to dithiol anchors in oligoacene and oligophenylene junctions.X-ray photoelectron spectroscopy(XPS)confirmed this bifurcation,linking the“short”and“long”groups to planar and skewed conformers,with dihedrals remarkably agreeing with the gas-phase values.This work establishes conformational bifurcation as a promising route for designing programmable nanotransport properties through anchor-group control.
基金Supported by the National Natural Science Foundation of China(Grant No.12371110).
文摘This paper is concerned with the following nonlinear Steklov problemΔu=0 in D,∂vu=λf(u)on∂D,where D is the unit disk in the plane,∂v denotes the unit outward normal derivative.For each k∈N,under some natural conditions on f,using the Crandall-Rabinowitz bifurcation theorem,we obtain a bifurcation curve emanating from(k,0).Furthermore,we also analyze the local structure of bifurcation curves and stability of solutions on them.Specifically,our results indicate the bifurcation is critical for each k and is subcritical(supercritical)if f'''(0)>0(f'''(0)<0).
基金Supported by the Guiding Project of Science and Technology Research Plan of Hubei Provincial Department of Education(B2022458)。
文摘One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.
基金supported by the National Natural Science Foundations of China(12371171)and the Natural Science Foundation of Jiangsu Province(BK20221339).
文摘We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272002 and 12372061)the R&D Program of Beijing Municipal Education Commission(Grant No.KM202310009004)+1 种基金the North China University of Technology(Grant No.2023XN075-01)the Youth Research Special Project of the North China University of Technology(Grant No.2025NCUTYRSP051)。
文摘This study investigates the bifurcation dynamics underlying rhythmic transitions in a biophysical hippocampal–cortical neural network model.We specifically focus on the membrane potential dynamics of excitatory neurons in the hippocampal CA3 region and examine how strong coupling parameters modulate memory consolidation processes.Employing bifurcation analysis,we systematically characterize the model's complex dynamical behaviors.Subsequently,a characteristic waveform recognition algorithm enables precise feature extraction and automated detection of hippocampal sharp-wave ripples(SWRs).Our results demonstrate that neuronal rhythms exhibit a propensity for abrupt transitions near bifurcation points,facilitating the emergence of SWRs.Critically,temporal rhythmic analysis reveals that the occurrence of a bifurcation is not always sufficient for SWR formation.By integrating one-parameter bifurcation analysis with extremum analysis,we demonstrate that large-amplitude membrane potential oscillations near bifurcation points are highly conducive to SWR generation.This research elucidates the mechanistic link between changes in neuronal self-connection parameters and the evolution of rhythmic characteristics,providing deeper insights into the role of dynamical behavior in memory consolidation.
基金Supported-by the National Natural Science Foundation of China(10471117)the Henan Innovation Project for University Prominent Research Talents(2005KYCX017)the Scientific Research Foundation of Education Ministry for the Returned Overseas Chinese Scholars
文摘In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution （xs（t）, O, zs（t）） is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period T the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.
基金Supported by the National Natural Science Foundation of China(11361047)Fundamental Research Program of Shanxi Province(20210302124529)。
文摘This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.
文摘As a typical biochemical reaction, the process of continuous fermentation of ethanol is studied in this paper. An improved model is set forward and in agreement with experiments. Nonlinear oscillations of the process are analyzed with analytical and numerical methods. The Hopf bifurcation region is fixed and further analyses are given.
文摘The transition boundaries of period doubling on the physical parameter plane of a Duffing system are obtained by the general Newton′s method, and the motion on different areas divided by transition boundaries is studied in this paper. When the physical parameters transpass the boundaries, the solutions of period T =2π/ω will lose their stability, and the solutions of period T =2π/ω take place. Continuous period doubling bifurcations lead to chaos.
