The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break...The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.展开更多
This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an ...This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.展开更多
A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics ...A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.展开更多
Dalan Formation is one of the most important gas reservoirs of south and southwest Iran which it belongs to Dehram Group and its age is Middle to Late Permian. The Dalan formation is interpreted as reflecting a major ...Dalan Formation is one of the most important gas reservoirs of south and southwest Iran which it belongs to Dehram Group and its age is Middle to Late Permian. The Dalan formation is interpreted as reflecting a major tectono-eustatic event related to the onset of rapid thermal subsidence of the early Neo-Tethys passive margin in Arabia and Iran, and the drowning of its rift shoulders. The Dalan formation consists mainly of medium to thick-bedded oolitic to micritic shallow-marine carbonate, with intercalations of evaporates. This formation overlies the Faraghan formation and extends up into the Lower Triassic kangan formation. The current paper is focused on the facies, sedimentary environment and sequence Stratigraphy study of the Middle to Upper Permian Dalan formation in the West Assaluyeh gas field the subsurface section of well ASL-A. Based on microfacies analysis and significant founa and flora, nineteen major facies in five facies associations including Tidal flat (A), Lagoon (B), Shoal (C), Open marine (D) and Mid ramp (E) were recognized in the Dalan formation. Facies analysis and those comparisons with modern and ancient environments indicated that the Dalan formation was deposited inner to mid parts of a homoclinal ramp. The sequence stratigraphy studies on the Dalan formation in this gas field led to assessment of seven main sedimentary sequences of the third-order in the Assaluyeh field, well ASL-A. The boundary between the third-order sequences with the Faraghan formation and between the Nar and Upper Dalan members are Subaerial Unconformity (SU) and the boundaries between the third-order sequences with each other and also with the Kangan formation are Correlative Conformity (CC). The main diagenetic processes in this formation are dolomitization, dissolution, anhydritization, cementation and compaction which played a significant role in improving reservoir quality. The shoal ooid grainstone facies with intergranular and oomoldic porosity comprise the main reservoir facies of the Dalan formation.展开更多
This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a...This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a nonlinear term.Since there are no periodic assumptions on L（t）and W（t,z）in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W（t,z）is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.展开更多
Early carboniferous deposits of the Kalmard block, with various characteristics in different outcrops, are recognized by Gachal Formation. Generally speaking, this formation comprises of four different members (A, B, ...Early carboniferous deposits of the Kalmard block, with various characteristics in different outcrops, are recognized by Gachal Formation. Generally speaking, this formation comprises of four different members (A, B, C and D), consisting of carbonate and evaporative rocks. Gachal Formation is composed chiefly of 55 meters sandstone and limestone interbedded with shale. According to the lithological and microscopic studies, Gachal Formation is deposited in beach, semi-restricted and open lagoon, shoal and open marine environments. Vertical changes of microfacies and the curve of its depth changes account for the high thickness of the facies of shoal and bar sub-environments and the low thickness of the facies of lagoon and open marine sub-environment as well. Gachal Formation rocks in Rahdar section are deposited in a low-angle?homoclinal ramp?located in southern Paleothysis Ocean. The carbonate-sandstone sequence in?Gachal Formation in Rahdar section is composed of a depositional sequence separated from each other by type 1 sequence boundaries. Deposits of this formation are separated from lower deposits by type 2 sequence boundary and from?Khan Group by unconformity. The sedimentary sequence identified in this formation points to the age of late Visean, conforming to Kaskaskia IV. The erosional boundary between Gachal and Khan Formations is relatively compatible with drop in sea level at Late Kaskaskia global scale.展开更多
The current paper is focused on the facies, sedimentary environment and depositional cycles study of the Middle-Late Permian sediments in the South Fars Zireh Gas Field, the subsurface section of well ZH-A. Four hundr...The current paper is focused on the facies, sedimentary environment and depositional cycles study of the Middle-Late Permian sediments in the South Fars Zireh Gas Field, the subsurface section of well ZH-A. Four hundred thin-sections obtained from cores and cuttings were examined under standard petrographic microscope. For this study research, Corel Draw X6, Corel Photo-Paint, DN2 Microscopy Image Processing System, Scope Photo, Autodesk Map, Geocalc and Auto Cad 2014 were utilized. Based on microfacies analysis and significant founa and flora, fourteen major facies in four facies associations comprising tidal flat (A), lagoon (B), shoal (C) and open marine (D) identified in the well ZH-A. This formation was deposited in inner part of a homoclinal ramp. Based on depositional cycles, seven main 3rd order sequences were revealed in the Well ZH-A. The ooid grainstone facies with interparticle and oomoldic porosity has high reservoir potential. The diagenetic processes like dolomitization and dissolution have significant effect in the reservoir quality. Based on research results, a major framework can be weaved and used to correlate reservoir layering.展开更多
A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The gene...A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.展开更多
By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by ...By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given.展开更多
The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutio...The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.展开更多
By using the method presented by G. Kovacic and S. Wiggins , the ordinary differential equation (ODE) on the generalized asymptotic inertial manifold(GAIM) of the sine Gordon equation is studied qualitatively. A...By using the method presented by G. Kovacic and S. Wiggins , the ordinary differential equation (ODE) on the generalized asymptotic inertial manifold(GAIM) of the sine Gordon equation is studied qualitatively. An analytical criterion for existence of orbits homoclinic to the resonance band is given. Under the same parametric values as ones in , by the method in , the existence of pulse orbits connecting to the resonance band is shown, and by comparing with the earlier results, this result explains the chaotic behavior observed in very well.展开更多
The homoclinic solutions problem of the Davey-Stewartson ( DS) Equations were studied. By using the Hirota's bilinear method, the homoclinic orbits of the Davey-Stewartson Equations were obtained through the depen...The homoclinic solutions problem of the Davey-Stewartson ( DS) Equations were studied. By using the Hirota's bilinear method, the homoclinic orbits of the Davey-Stewartson Equations were obtained through the dependent variable transformation. The homoclinic orbits of the Davey-Stewartson Equations were discussed.展开更多
By means of an extension of Mawhin＇s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, ...By means of an extension of Mawhin＇s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.展开更多
The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neit...The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.展开更多
To continue the discussion in （Ⅰ ） and （ Ⅱ ）,and finish the study of the limit cycle problem for quadratic system （ Ⅲ ）m=0 in this paper. Since there is at most one limit cycle that may be created from critic...To continue the discussion in （Ⅰ ） and （ Ⅱ ）,and finish the study of the limit cycle problem for quadratic system （ Ⅲ ）m=0 in this paper. Since there is at most one limit cycle that may be created from critical point O by Hopf bifurcation,the number of limit cycles depends on the different situations of separatrix cycle to be formed around O. If it is a homoclinic cycle passing through saddle S1 on 1 ＋ax-y = 0,which has the same stability with the limit cycle created by Hopf bifurcation,then the uniqueness of limit cycles in such cases can be proved. If it is a homoclinic cycle passing through saddle N on x= 0,which has the different stability from the limit cycle created by Hopf bifurcation,then it will be a case of two limit cycles. For the case when the separatrix cycle is a heteroclinic cycle passing through two saddles at infinity,the discussion of the paper shows that the number of limit cycles will change from one to two depending on the different values of parameters of system.展开更多
In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonli...In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.展开更多
This paper mainly discusses the existence of nontrivial homoclinic solutions for nonperiodic semilinear fourth-order ordinary differential equation u^（4）＋pu″＋a（x）u-b（x）u^2=c（x）u^3=3arising in the study of p...This paper mainly discusses the existence of nontrivial homoclinic solutions for nonperiodic semilinear fourth-order ordinary differential equation u^（4）＋pu″＋a（x）u-b（x）u^2=c（x）u^3=3arising in the study of pattern formation by means of Mountain Pass Lemma.展开更多
In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear eq...In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.展开更多
It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-d...It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.展开更多
In this article, using multi-parameter perturbation theory and qualitative analysis, the authors studied a kind of cubic system perturbed by degree five and ob-tained the system that can have 17 limit cycles giving th...In this article, using multi-parameter perturbation theory and qualitative analysis, the authors studied a kind of cubic system perturbed by degree five and ob-tained the system that can have 17 limit cycles giving their two kinds of distributions (see Fig.5).展开更多
基金support from the National Natural Science Foundation of China(Nos.12102242 and 12172086)the Educational Foundation of Liaoning Province(No.JYTQN2023261)the Key R&D Program of Shandong Province of China(No.2022SFGC0801).
文摘The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.
基金supported by the National Natural Science Foundation of China(Grant No.12171253).
文摘This paper is concerned with the existence of nontrivial homoclinic solutions for a class of second order Hamiltonian systems with external forc-ing perturbations q+Aq+Vq(t,q)=f(t),where q=(q1,q2,..qN)∈R^(N),A is an antisymmetric constant N×N matrix,V(t,q)=-K(t,q)+W(t,q)with K,W ∈C^(1)(R,R^(N))and satisfying b1|q|^(2)≤K(t,q)≤b_(2)|q|^(2)for some positive constants b_(2)≥b_(1)>0 and external forcing term f∈C(R,R^(N))being small enough.Under some new weak superquadratic conditions for W,by using the mountain pass theorem,we obtain the existence of at least one nontrivial homoclinic solution.
文摘A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.
文摘Dalan Formation is one of the most important gas reservoirs of south and southwest Iran which it belongs to Dehram Group and its age is Middle to Late Permian. The Dalan formation is interpreted as reflecting a major tectono-eustatic event related to the onset of rapid thermal subsidence of the early Neo-Tethys passive margin in Arabia and Iran, and the drowning of its rift shoulders. The Dalan formation consists mainly of medium to thick-bedded oolitic to micritic shallow-marine carbonate, with intercalations of evaporates. This formation overlies the Faraghan formation and extends up into the Lower Triassic kangan formation. The current paper is focused on the facies, sedimentary environment and sequence Stratigraphy study of the Middle to Upper Permian Dalan formation in the West Assaluyeh gas field the subsurface section of well ASL-A. Based on microfacies analysis and significant founa and flora, nineteen major facies in five facies associations including Tidal flat (A), Lagoon (B), Shoal (C), Open marine (D) and Mid ramp (E) were recognized in the Dalan formation. Facies analysis and those comparisons with modern and ancient environments indicated that the Dalan formation was deposited inner to mid parts of a homoclinal ramp. The sequence stratigraphy studies on the Dalan formation in this gas field led to assessment of seven main sedimentary sequences of the third-order in the Assaluyeh field, well ASL-A. The boundary between the third-order sequences with the Faraghan formation and between the Nar and Upper Dalan members are Subaerial Unconformity (SU) and the boundaries between the third-order sequences with each other and also with the Kangan formation are Correlative Conformity (CC). The main diagenetic processes in this formation are dolomitization, dissolution, anhydritization, cementation and compaction which played a significant role in improving reservoir quality. The shoal ooid grainstone facies with intergranular and oomoldic porosity comprise the main reservoir facies of the Dalan formation.
文摘This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a nonlinear term.Since there are no periodic assumptions on L（t）and W（t,z）in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W（t,z）is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.
文摘Early carboniferous deposits of the Kalmard block, with various characteristics in different outcrops, are recognized by Gachal Formation. Generally speaking, this formation comprises of four different members (A, B, C and D), consisting of carbonate and evaporative rocks. Gachal Formation is composed chiefly of 55 meters sandstone and limestone interbedded with shale. According to the lithological and microscopic studies, Gachal Formation is deposited in beach, semi-restricted and open lagoon, shoal and open marine environments. Vertical changes of microfacies and the curve of its depth changes account for the high thickness of the facies of shoal and bar sub-environments and the low thickness of the facies of lagoon and open marine sub-environment as well. Gachal Formation rocks in Rahdar section are deposited in a low-angle?homoclinal ramp?located in southern Paleothysis Ocean. The carbonate-sandstone sequence in?Gachal Formation in Rahdar section is composed of a depositional sequence separated from each other by type 1 sequence boundaries. Deposits of this formation are separated from lower deposits by type 2 sequence boundary and from?Khan Group by unconformity. The sedimentary sequence identified in this formation points to the age of late Visean, conforming to Kaskaskia IV. The erosional boundary between Gachal and Khan Formations is relatively compatible with drop in sea level at Late Kaskaskia global scale.
文摘The current paper is focused on the facies, sedimentary environment and depositional cycles study of the Middle-Late Permian sediments in the South Fars Zireh Gas Field, the subsurface section of well ZH-A. Four hundred thin-sections obtained from cores and cuttings were examined under standard petrographic microscope. For this study research, Corel Draw X6, Corel Photo-Paint, DN2 Microscopy Image Processing System, Scope Photo, Autodesk Map, Geocalc and Auto Cad 2014 were utilized. Based on microfacies analysis and significant founa and flora, fourteen major facies in four facies associations comprising tidal flat (A), lagoon (B), shoal (C) and open marine (D) identified in the well ZH-A. This formation was deposited in inner part of a homoclinal ramp. Based on depositional cycles, seven main 3rd order sequences were revealed in the Well ZH-A. The ooid grainstone facies with interparticle and oomoldic porosity has high reservoir potential. The diagenetic processes like dolomitization and dissolution have significant effect in the reservoir quality. Based on research results, a major framework can be weaved and used to correlate reservoir layering.
基金supported by the National Natural Science Foundation of China (10672193)Sun Yat-sen University (Fu Lan Scholarship)the University of Hong Kong (CRGC grant).
文摘A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.
基金supported by the National Natural Science Foundation of China (Grant 11172199)
文摘By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given.
基金Supported by the Natural Science Foundation of China under Grant Nos.10361007,10661002Yunnan Natural Science Foundation under Grant No.2006A0082M
文摘The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.
文摘By using the method presented by G. Kovacic and S. Wiggins , the ordinary differential equation (ODE) on the generalized asymptotic inertial manifold(GAIM) of the sine Gordon equation is studied qualitatively. An analytical criterion for existence of orbits homoclinic to the resonance band is given. Under the same parametric values as ones in , by the method in , the existence of pulse orbits connecting to the resonance band is shown, and by comparing with the earlier results, this result explains the chaotic behavior observed in very well.
文摘The homoclinic solutions problem of the Davey-Stewartson ( DS) Equations were studied. By using the Hirota's bilinear method, the homoclinic orbits of the Davey-Stewartson Equations were obtained through the dependent variable transformation. The homoclinic orbits of the Davey-Stewartson Equations were discussed.
基金sponsored by the National Natural Science Foundation of China(11271197)the Science and Technology Foundation in Ministry of Education of China(207047)the Science Foundation of NUIST of China(20090202 and 2012r101)
文摘By means of an extension of Mawhin＇s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.
基金Supported by National Natural Science Foundation of China (10771173)
文摘The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.
基金Project supported by the National Natural Science Foundation of China （10471066）.
文摘To continue the discussion in （Ⅰ ） and （ Ⅱ ）,and finish the study of the limit cycle problem for quadratic system （ Ⅲ ）m=0 in this paper. Since there is at most one limit cycle that may be created from critical point O by Hopf bifurcation,the number of limit cycles depends on the different situations of separatrix cycle to be formed around O. If it is a homoclinic cycle passing through saddle S1 on 1 ＋ax-y = 0,which has the same stability with the limit cycle created by Hopf bifurcation,then the uniqueness of limit cycles in such cases can be proved. If it is a homoclinic cycle passing through saddle N on x= 0,which has the different stability from the limit cycle created by Hopf bifurcation,then it will be a case of two limit cycles. For the case when the separatrix cycle is a heteroclinic cycle passing through two saddles at infinity,the discussion of the paper shows that the number of limit cycles will change from one to two depending on the different values of parameters of system.
基金Supported by the Natural Science Foundation of China under Grant No. 10971169Sichuan Educational Science Foundation under Grant No. 09zc008
文摘In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.
基金The Project sponsored by SRF for ROCS, SEM"985 Engineer" of China (CUN 985-3-3)
文摘This paper mainly discusses the existence of nontrivial homoclinic solutions for nonperiodic semilinear fourth-order ordinary differential equation u^（4）＋pu″＋a（x）u-b（x）u^2=c（x）u^3=3arising in the study of pattern formation by means of Mountain Pass Lemma.
文摘In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.
文摘It this paper we obtain existence and bifurcation theorems for homoclinic orbits in three-dimeensional,time dependent and independent,perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds.Thed we apply them to a truncated spectral model of the quasi-geostrophic flow on a cyclic β-plane.
基金Surported by the Foundation of Shandong University of Technology (2006KJM01)
文摘In this article, using multi-parameter perturbation theory and qualitative analysis, the authors studied a kind of cubic system perturbed by degree five and ob-tained the system that can have 17 limit cycles giving their two kinds of distributions (see Fig.5).
