Bifurcations of nontwisted and fine heteroclinic loops are studied for higher dimensional systems. The existence and its associated existing regions are given for the 1-hom orbit and the 1-per orbit, respectively, and...Bifurcations of nontwisted and fine heteroclinic loops are studied for higher dimensional systems. The existence and its associated existing regions are given for the 1-hom orbit and the 1-per orbit, respectively, and bifurcation surfaces of the two-fold periodic orbit are also obtained. At last, these bifurcation results are applied to the fine heteroclinic loop for the planar system, which leads to some new and interesting results.展开更多
In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical sys...In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view.It is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is given.Furthermore,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered.展开更多
Periodic orbits are crucial in facilitating the understanding of the dynamical behavior of elongated asteroids.As a specific type of periodic orbit,resonant orbits can enrich the orbit design method of deep-space expl...Periodic orbits are crucial in facilitating the understanding of the dynamical behavior of elongated asteroids.As a specific type of periodic orbit,resonant orbits can enrich the orbit design method of deep-space exploration missions.Herein,a dipole segment model for investigating the orbital dynamics of elongated asteroids is briefly introduced.A new numerical algorithm named the modified path searching method for identifying spin-orbit resonant orbits is proposed.Using the modified path searching and pseudo-arclength continuation methods,four spin-orbit resonant families for asteroid 2063 Bacchus are obtained.The distribution of eigenvalues and stability curves for the four resonant families are presented.In particular,some critical points corresponding to period-doubling and tangent bifurcations appear in the stability curves.展开更多
We have successfully demonstrated a 1 Kb spin-orbit torque(SOT)magnetic random-access memory(MRAM)multiplexer(MUX)array with remarkable performance.The 1 Kb MUX array exhibits an in-die function yield of over 99.6%.Ad...We have successfully demonstrated a 1 Kb spin-orbit torque(SOT)magnetic random-access memory(MRAM)multiplexer(MUX)array with remarkable performance.The 1 Kb MUX array exhibits an in-die function yield of over 99.6%.Additionally,it provides a sufficient readout window,with a TMR/RP_sigma%value of 21.4.Moreover,the SOT magnetic tunnel junctions(MTJs)in the array show write error rates as low as 10^(-6)without any ballooning effects or back-hopping behaviors,ensuring the write stability and reliability.This array achieves write operations in 20 ns and 1.2 V for an industrial-level temperature range from-40 to 125℃.Overall,the demonstrated array shows competitive specifications compared to the state-of-the-art works.Our work paves the way for the industrial-scale production of SOT-MRAM,moving this technology beyond R&D and towards widespread adoption.展开更多
During dynamic walking of biped robots, the underactuated rotating degree of freedom （DOF） emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addres...During dynamic walking of biped robots, the underactuated rotating degree of freedom （DOF） emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addresses the asymptotic orbit stability for dimension-variant hybrid systems （DVHS）. Based on the generalized Poincare map, the stability criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with fiat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed method.展开更多
In this paper,three competitive systems with different kinds of state-dependent control are presented and investigated.The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems tha...In this paper,three competitive systems with different kinds of state-dependent control are presented and investigated.The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory,and the stability of the order-1 periodic solution of each system is also given.Besides,sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincare criterion,respectively.Finally,numerical simulations are carried out to verify the theoretical results.展开更多
文摘Bifurcations of nontwisted and fine heteroclinic loops are studied for higher dimensional systems. The existence and its associated existing regions are given for the 1-hom orbit and the 1-per orbit, respectively, and bifurcation surfaces of the two-fold periodic orbit are also obtained. At last, these bifurcation results are applied to the fine heteroclinic loop for the planar system, which leads to some new and interesting results.
文摘In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view.It is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is given.Furthermore,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered.
基金supported partially by the National Natural Science Foundation of China(Grant Nos.11772009 and 12172013)the Beijing Municipal Natural Science Foundation(Grant No.1192002).
文摘Periodic orbits are crucial in facilitating the understanding of the dynamical behavior of elongated asteroids.As a specific type of periodic orbit,resonant orbits can enrich the orbit design method of deep-space exploration missions.Herein,a dipole segment model for investigating the orbital dynamics of elongated asteroids is briefly introduced.A new numerical algorithm named the modified path searching method for identifying spin-orbit resonant orbits is proposed.Using the modified path searching and pseudo-arclength continuation methods,four spin-orbit resonant families for asteroid 2063 Bacchus are obtained.The distribution of eigenvalues and stability curves for the four resonant families are presented.In particular,some critical points corresponding to period-doubling and tangent bifurcations appear in the stability curves.
基金supported by the National Key Research and Development Program of China (Nos.2021YFB3601303,2021YFB3601304,2021YFB3601300,2022YFB4400200,2022YFB4400201,2022YFB4400203)the National Natural Science Foundation of China (Grant No.62171013)。
文摘We have successfully demonstrated a 1 Kb spin-orbit torque(SOT)magnetic random-access memory(MRAM)multiplexer(MUX)array with remarkable performance.The 1 Kb MUX array exhibits an in-die function yield of over 99.6%.Additionally,it provides a sufficient readout window,with a TMR/RP_sigma%value of 21.4.Moreover,the SOT magnetic tunnel junctions(MTJs)in the array show write error rates as low as 10^(-6)without any ballooning effects or back-hopping behaviors,ensuring the write stability and reliability.This array achieves write operations in 20 ns and 1.2 V for an industrial-level temperature range from-40 to 125℃.Overall,the demonstrated array shows competitive specifications compared to the state-of-the-art works.Our work paves the way for the industrial-scale production of SOT-MRAM,moving this technology beyond R&D and towards widespread adoption.
基金the National Natural Science Foundation of China (No. 50575119)the 863 Program(No. 2006AA04Z253)the Ph.D.Programs Foundation of Ministry of Education of China(No. 20060003026)
文摘During dynamic walking of biped robots, the underactuated rotating degree of freedom （DOF） emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addresses the asymptotic orbit stability for dimension-variant hybrid systems （DVHS）. Based on the generalized Poincare map, the stability criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with fiat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed method.
基金The authors would like to thank the anonymous referees and Professor Lansun Chen for their very valuable comments,which led to a significant improveinent of the original paper.This work is supposed by the National Natural Science Foundation of China(No.11671346)Nanhu Scholars Program of XYNU.
文摘In this paper,three competitive systems with different kinds of state-dependent control are presented and investigated.The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory,and the stability of the order-1 periodic solution of each system is also given.Besides,sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincare criterion,respectively.Finally,numerical simulations are carried out to verify the theoretical results.
