We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In ...We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits decreases.Fur-ther, the periodic orbits around Saturn and Sun moves towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observed.展开更多
In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit i...In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Si＇lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.展开更多
In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dime...In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dimensional continuous maps with certain specific periodic points.Further, we obtain results for the existence of chaotic phenomenon in the sense of Li and Yorke. Some examples are also analyzed using the proposed methods.展开更多
In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chao...In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results.展开更多
This paper proposes a method for constructing partial differential equation (PDE) systems with chaotic solitons by using truncated normal forms of an ordinary differential equation (ODE). The construction is based mai...This paper proposes a method for constructing partial differential equation (PDE) systems with chaotic solitons by using truncated normal forms of an ordinary differential equation (ODE). The construction is based mainly on the fact that the existence of a soliton in a PDE system is equal to that of a homoclinic orbit in a related ODE system, and that chaos of ?i’lnikov homoclinic type in the ODE imply that the soliton in the PDE changes its profile chaotically along propagation direction. It is guaranteed that the constructed systems can self-generate chaotic solitons without any external perturbation but with constrained wave velocities in a rigorously mathematical sense.展开更多
Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic ...Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.展开更多
Secure and high-speed optical communications are of primary focus in information transmission.Although it is widely accepted that chaotic secure communication can provide superior physical layer security,it is challen...Secure and high-speed optical communications are of primary focus in information transmission.Although it is widely accepted that chaotic secure communication can provide superior physical layer security,it is challenging to meet the demand for high-speed increasing communication rate.We theoretically propose and experimentally demonstrate a conceptual paradigm for orbital angular momentum(OAM)configured chaotic laser(OAM-CCL)that allows access to high-security and massivecapacity optical communications.Combining 11 OAM modes and an all-optical feedback chaotic laser,we are able to theoretically empower a well-defined optical communication system with a total transmission capacity of 100 Gb∕s and a bit error rate below the forward error correction threshold 3.8×10^(-3).Furthermore,the OAM-CCL-based communication system is robust to 3D misalignment by resorting to appropriate mode spacing and beam waist.Finally,the conceptual paradigm of the OAM-CCL-based communication system is verified.In contrast to existing systems(traditional free-space optical communication or chaotic optical communication),the OAM-CCL-based communication system has threein-one characteristics of high security,massive capacity,and robustness.The findings demonstrate that this will promote the applicable settings of chaotic laser and provide an alternative promising route to guide high-security and massive-capacity optical communications.展开更多
文摘We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits decreases.Fur-ther, the periodic orbits around Saturn and Sun moves towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61170037 and 61074192)
文摘In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Si＇lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.
文摘In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dimensional continuous maps with certain specific periodic points.Further, we obtain results for the existence of chaotic phenomenon in the sense of Li and Yorke. Some examples are also analyzed using the proposed methods.
基金supported by the Beijing Natural Science Foundation,China(Grant No.4132005)the National Natural Science Foundation of China(Grant No.61403006)+1 种基金the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions,China(Grant No.YETP1449)the Project of Scientific and Technological Innovation Platform,China(Grant No.PXM2015 014213 000063)
文摘In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results.
文摘This paper proposes a method for constructing partial differential equation (PDE) systems with chaotic solitons by using truncated normal forms of an ordinary differential equation (ODE). The construction is based mainly on the fact that the existence of a soliton in a PDE system is equal to that of a homoclinic orbit in a related ODE system, and that chaos of ?i’lnikov homoclinic type in the ODE imply that the soliton in the PDE changes its profile chaotically along propagation direction. It is guaranteed that the constructed systems can self-generate chaotic solitons without any external perturbation but with constrained wave velocities in a rigorously mathematical sense.
文摘Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.
基金supported by the National Natural Science Foundation of China(Grant Nos.61927811,62035009,and 11974258)the Fundamental Research Program of Shanxi Province(Grant No.202103021224038)+3 种基金the Development Fund in Science and Technology of Shanxi Province(Grant No.YDZJSX2021A009)the Open Fund of State Key Laboratory of Applied Optics(Grant No.SKLAO2022001A09)the Science and Technology Foundation of Guizhou Province(Grant Nos.ZK[2021]031 and ZK[2023]049)the Program for Guangdong Introducing Innovative and Entrepreneurial Teams.
文摘Secure and high-speed optical communications are of primary focus in information transmission.Although it is widely accepted that chaotic secure communication can provide superior physical layer security,it is challenging to meet the demand for high-speed increasing communication rate.We theoretically propose and experimentally demonstrate a conceptual paradigm for orbital angular momentum(OAM)configured chaotic laser(OAM-CCL)that allows access to high-security and massivecapacity optical communications.Combining 11 OAM modes and an all-optical feedback chaotic laser,we are able to theoretically empower a well-defined optical communication system with a total transmission capacity of 100 Gb∕s and a bit error rate below the forward error correction threshold 3.8×10^(-3).Furthermore,the OAM-CCL-based communication system is robust to 3D misalignment by resorting to appropriate mode spacing and beam waist.Finally,the conceptual paradigm of the OAM-CCL-based communication system is verified.In contrast to existing systems(traditional free-space optical communication or chaotic optical communication),the OAM-CCL-based communication system has threein-one characteristics of high security,massive capacity,and robustness.The findings demonstrate that this will promote the applicable settings of chaotic laser and provide an alternative promising route to guide high-security and massive-capacity optical communications.
