In this paper, following the phase portraits analysis, we investigate the integrability of a system which physically describes the transverse oscillation of an elastic beam under end-thrust. As a result, we find that ...In this paper, following the phase portraits analysis, we investigate the integrability of a system which physically describes the transverse oscillation of an elastic beam under end-thrust. As a result, we find that this system actually comprises two families of travelling waves： the sub- and super-sonic periodic waves of positive- and negative- definite velocities, respectively, and the localized sub-sonic loop-shaped waves of positive-definite velocity. Expressing the energy-like of this system while depicting its phase portrait dynamics, we show that these multivaiued localized travelling waves appear as the boundary solutions to which the periodic travelling waves tend asymptotically展开更多
The global phase portrait describes the qualitative behaviour of the solution set for all time. In general, this is as close as we can get to solving nonlinear systems. The question of particular interest is: For what...The global phase portrait describes the qualitative behaviour of the solution set for all time. In general, this is as close as we can get to solving nonlinear systems. The question of particular interest is: For what parameter values does the global phase portrait of a dynamical system change its qualitative structure? In this paper, we attempt to answer the above question specifically for the case of certain third order nonlinear differential equations of the form . The linear case where is also considered. Our phase portrait analysis shows that under certain conditions on the coefficients as well as the function , we have asymptotic stability of solutions.展开更多
Influence of recombination centers’ changes on the form of phase portraits has been studied. It has been shown that the shape of the phase portraits depends on the concentration of semiconductor materials’ recombina...Influence of recombination centers’ changes on the form of phase portraits has been studied. It has been shown that the shape of the phase portraits depends on the concentration of semiconductor materials’ recombination centers.展开更多
Theoretical investigation of generation-recombination processes in silicon, which has a lifetime of charge carriers 10-3 s and capture cross sections of 10-16 sm2. For the study uses a method of phase portraits, which...Theoretical investigation of generation-recombination processes in silicon, which has a lifetime of charge carriers 10-3 s and capture cross sections of 10-16 sm2. For the study uses a method of phase portraits, which are widely used in the theory of vibrations. It is shown that the form of phase portraits strongly depends on the frequency of exposure to the external variable deformation.展开更多
This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator.Such systems have the form x=-y+xf(x,y),y=x+yf(x,y),where f(x,y)=a_(1)x+a_(2)xy+a_(3)xy^(2)+...This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator.Such systems have the form x=-y+xf(x,y),y=x+yf(x,y),where f(x,y)=a_(1)x+a_(2)xy+a_(3)xy^(2)+a_(4)xy^(3)+a_(5)xy^(4)=xσ(y),and any zero of 1+a_(1)y+a_(2)y^(2)+a_(3)y^(3)+a_(4)y^(4)+a_(5)y^(5),y=y is an invariant straight line.At last,all global phase portraits are drawn on the Poincare disk.展开更多
The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular...The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.展开更多
In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex e...In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 ＋ y^2 ＋ 1 = 0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincare disc.展开更多
This paper deals with the bifurcations and phase portraits of an asymmetric triaxial gyrostat with two rotors, which is a 3-dimensional generalized Hamiltonian system with a quadratic Hamiltonian depending on three in...This paper deals with the bifurcations and phase portraits of an asymmetric triaxial gyrostat with two rotors, which is a 3-dimensional generalized Hamiltonian system with a quadratic Hamiltonian depending on three independent parameters. The number and stability of equilibria are analyzed, and corresponding bifurcation conditions of parameters are obtained. Moreover, by Maple software, all possible phase portraits are plotted out. Except for some planar orbits under particular parametric conditions, general orbits can not be expressed in terms of elementary or elliptic functions.展开更多
In this paper,a quartic Hamiltonian system with Z5-equivariant property is considered.Using the methods of qualitative analysis,bifurcations of the above system are analyzed,the phase portraits of the system are class...In this paper,a quartic Hamiltonian system with Z5-equivariant property is considered.Using the methods of qualitative analysis,bifurcations of the above system are analyzed,the phase portraits of the system are classified and representative orbits are shown by Maple software.展开更多
In this paper, we consider the Z8-equivariant planar Hamiltonian vector field of degree 7. By using the qualitative and numerical computation, we divide the parameters space into six-parameter-space. And we obtain the...In this paper, we consider the Z8-equivariant planar Hamiltonian vector field of degree 7. By using the qualitative and numerical computation, we divide the parameters space into six-parameter-space. And we obtain the results as following : 1. There are seven cases of the number of fixed point of above vector field in finite part, that is, 1,9,l7,25,4l,49, respectively. 2. The possible phase portraits of this vector field are fifty.展开更多
Spiking neural networks(SNNs)represent a biologically-inspired computational framework that bridges neuroscience and artificial intelligence,offering unique advantages in temporal data processing,energy efficiency,and...Spiking neural networks(SNNs)represent a biologically-inspired computational framework that bridges neuroscience and artificial intelligence,offering unique advantages in temporal data processing,energy efficiency,and real-time decision-making.This paper explores the evolution of SNN technologies,emphasizing their integration with advanced learning mechanisms such as spike-timing-dependent plasticity(STDP)and hybridization with deep learning architectures.Leveraging memristors as nanoscale synaptic devices,we demonstrate significant enhancements in energy efficiency,adaptability,and scalability,addressing key challenges in neuromorphic computing.Through phase portraits and nonlinear dynamics analysis,we validate the system’s stability and robustness under diverse workloads.These advancements position SNNs as a transformative technology for applications in robotics,IoT,and adaptive low-power AI systems,paving the way for future innovations in neuromorphic hardware and hybrid learning paradigms.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
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
文摘In this paper, following the phase portraits analysis, we investigate the integrability of a system which physically describes the transverse oscillation of an elastic beam under end-thrust. As a result, we find that this system actually comprises two families of travelling waves： the sub- and super-sonic periodic waves of positive- and negative- definite velocities, respectively, and the localized sub-sonic loop-shaped waves of positive-definite velocity. Expressing the energy-like of this system while depicting its phase portrait dynamics, we show that these multivaiued localized travelling waves appear as the boundary solutions to which the periodic travelling waves tend asymptotically
文摘The global phase portrait describes the qualitative behaviour of the solution set for all time. In general, this is as close as we can get to solving nonlinear systems. The question of particular interest is: For what parameter values does the global phase portrait of a dynamical system change its qualitative structure? In this paper, we attempt to answer the above question specifically for the case of certain third order nonlinear differential equations of the form . The linear case where is also considered. Our phase portrait analysis shows that under certain conditions on the coefficients as well as the function , we have asymptotic stability of solutions.
文摘Influence of recombination centers’ changes on the form of phase portraits has been studied. It has been shown that the shape of the phase portraits depends on the concentration of semiconductor materials’ recombination centers.
文摘Theoretical investigation of generation-recombination processes in silicon, which has a lifetime of charge carriers 10-3 s and capture cross sections of 10-16 sm2. For the study uses a method of phase portraits, which are widely used in the theory of vibrations. It is shown that the form of phase portraits strongly depends on the frequency of exposure to the external variable deformation.
基金supported by National Natural Science Foundation of China(No.12301197)Natural Science Foundation of Henan(No.232300420343)+2 种基金Science and Technology Research Project of Henan Province(No.232102210057)Scientific Research Foundation for Doctoral Scholars of Haust(No.13480077)Natural Science Foundation of Hunan(No.2021JJ30166)。
文摘This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator.Such systems have the form x=-y+xf(x,y),y=x+yf(x,y),where f(x,y)=a_(1)x+a_(2)xy+a_(3)xy^(2)+a_(4)xy^(3)+a_(5)xy^(4)=xσ(y),and any zero of 1+a_(1)y+a_(2)y^(2)+a_(3)y^(3)+a_(4)y^(4)+a_(5)y^(5),y=y is an invariant straight line.At last,all global phase portraits are drawn on the Poincare disk.
基金Supported by Ministerio de Ciencia y Tecnología,Plan Nacional I+D+I co-financed with FEDER funds,in the frame of the pro jects MTM2010-20907-C02-02by Consejería de Educación y Ciencia de la Junta de Andalucía(Grant Nos.FQM-276 and P08-FQM-03770)
文摘The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.
基金partially supported by a MINECO/FEDER grant MTM2013-40998-Pan AGAUR grant number 2014 SGR568+2 种基金the grants FP7-PEOPLE-2012-IRSES 318999 and 316338the MINECO/FEDER grant UNAB13-4E-1604partially supported by FCT/Portugal through UID/MAT/04459/2013
文摘In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 ＋ y^2 ＋ 1 = 0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincare disc.
基金supported by the NNSF of China under Grant No.10872183
文摘This paper deals with the bifurcations and phase portraits of an asymmetric triaxial gyrostat with two rotors, which is a 3-dimensional generalized Hamiltonian system with a quadratic Hamiltonian depending on three independent parameters. The number and stability of equilibria are analyzed, and corresponding bifurcation conditions of parameters are obtained. Moreover, by Maple software, all possible phase portraits are plotted out. Except for some planar orbits under particular parametric conditions, general orbits can not be expressed in terms of elementary or elliptic functions.
文摘In this paper,a quartic Hamiltonian system with Z5-equivariant property is considered.Using the methods of qualitative analysis,bifurcations of the above system are analyzed,the phase portraits of the system are classified and representative orbits are shown by Maple software.
基金National Natural Science Fundation of P.R.China (10071097).
文摘In this paper, we consider the Z8-equivariant planar Hamiltonian vector field of degree 7. By using the qualitative and numerical computation, we divide the parameters space into six-parameter-space. And we obtain the results as following : 1. There are seven cases of the number of fixed point of above vector field in finite part, that is, 1,9,l7,25,4l,49, respectively. 2. The possible phase portraits of this vector field are fifty.
基金Supported by CUP(J53C22003010006,J43C24000230007)ICREA2019.
文摘Spiking neural networks(SNNs)represent a biologically-inspired computational framework that bridges neuroscience and artificial intelligence,offering unique advantages in temporal data processing,energy efficiency,and real-time decision-making.This paper explores the evolution of SNN technologies,emphasizing their integration with advanced learning mechanisms such as spike-timing-dependent plasticity(STDP)and hybridization with deep learning architectures.Leveraging memristors as nanoscale synaptic devices,we demonstrate significant enhancements in energy efficiency,adaptability,and scalability,addressing key challenges in neuromorphic computing.Through phase portraits and nonlinear dynamics analysis,we validate the system’s stability and robustness under diverse workloads.These advancements position SNNs as a transformative technology for applications in robotics,IoT,and adaptive low-power AI systems,paving the way for future innovations in neuromorphic hardware and hybrid learning paradigms.
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.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
