In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with ...In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.展开更多
This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability ...This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.展开更多
In this study,the output tracking of delayed logical control networks(DLCNs)with state and control constraints is further investigated.Compared with other delays,state-dependent delay updates its value depending on th...In this study,the output tracking of delayed logical control networks(DLCNs)with state and control constraints is further investigated.Compared with other delays,state-dependent delay updates its value depending on the current state values and a pseudo-logical function.Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned.Using the semi-tensor product of matrices,dynamical equations of DLCNs are converted into an algebraic description,and an equivalent augmented system is constructed.Based on the augmented system,the output tracking problem is transformed into a set stabilization problem.A deformation of the state transition matrix is computed,and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint.This condition is easily verified by mathematical software.In addition,the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal.Finally,theoretical results are illustrated by an example.展开更多
By utilizing the Krasnoselskii＇s fixed point theorem in cones we obtain some sufficient conditions which guarantee the existence of positive periodic solution for a class of differential equations with state-dependen...By utilizing the Krasnoselskii＇s fixed point theorem in cones we obtain some sufficient conditions which guarantee the existence of positive periodic solution for a class of differential equations with state-dependent delays. The results in the papers [1,2] have been improved.展开更多
In general, earthquake cycle related to earthquake faulting could include four major processes which could be described by （1） fault locking, （2） self-acceleration or nucleation （possible foreshocks）, （3） cose...In general, earthquake cycle related to earthquake faulting could include four major processes which could be described by （1） fault locking, （2） self-acceleration or nucleation （possible foreshocks）, （3） coseismic slip, and （4） post-stress relaxation and afterslip. A sudden static stress change/perturbation in the surrounding crust can advance/ delay the fault instability or failure time and modify earth- quake rates. Based on a simple one-dimensional spring-sli- der block model with the combination of rate-and-state- dependent friction relation, in this study, we have approxi- mately derived the simple analytical solutions of clock advance/delay of fault failures caused by a sudden static Coulomb stress change applied in the different temporal evolution periods during an earthquake faulting. The results have been used in the physics-based explanation of delayed characteristic earthquake in Parkfield region, California, in which the next characteristic earthquake of M 6.0 after 1966 occurred in 2004 instead of around 1988 according to its characteristic return period of 22 years. At the same time, the analytical solutions also indicate that the time advance/ delay in Coulomb stress change derived by the dislocation model has a certain limitation and fundamental flaw. Fur- thermore, we discussed the essential difference between rate- and state-variable constitutive （R-S） model and Coulomb stress model used commonly in current earthquake triggering study, and demonstrated that, in fact, the Coulomb stress model could be involved in the R-S model. The results, we have obtained in this study, could be used in the development of time-dependent fault interaction model and the probability calculation related to the time-dependent and renewal earthquake prediction model.展开更多
This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay,which is assumed to be an increasing function of the population density with l...This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay,which is assumed to be an increasing function of the population density with lower and upper bound.Especially,state-dependent delay is introduced into a nonlocal reaction-diffusion model.The conditions of Schauder's fixed point theorem are proved by constructing a reasonable set of functionsΓ(see Section 2)and a pair of upper-lower solutions,so the existence of traveling wavefronts is established.The present study is continuation of a previous work that highlights the Laplacian diffusion.展开更多
This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theori...This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.展开更多
文摘In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.
文摘This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.
基金Project supported by the National Natural Science Foundation of China(Nos.61773371 and 61877036)the Natural Science Foundation of Shandong Province,China(No.ZR2019MF002)。
文摘In this study,the output tracking of delayed logical control networks(DLCNs)with state and control constraints is further investigated.Compared with other delays,state-dependent delay updates its value depending on the current state values and a pseudo-logical function.Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned.Using the semi-tensor product of matrices,dynamical equations of DLCNs are converted into an algebraic description,and an equivalent augmented system is constructed.Based on the augmented system,the output tracking problem is transformed into a set stabilization problem.A deformation of the state transition matrix is computed,and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint.This condition is easily verified by mathematical software.In addition,the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal.Finally,theoretical results are illustrated by an example.
基金Project supported by the Scientific Research foundation of Fujian Province (No.Z0511026).
文摘By utilizing the Krasnoselskii＇s fixed point theorem in cones we obtain some sufficient conditions which guarantee the existence of positive periodic solution for a class of differential equations with state-dependent delays. The results in the papers [1,2] have been improved.
基金This work is supported by the National Natural Sciences Foundation of People’s Republic of China under Grant(10061004)The Natural Sciences Foundation of Yunnan Province(2000A0001M)
文摘In general, earthquake cycle related to earthquake faulting could include four major processes which could be described by （1） fault locking, （2） self-acceleration or nucleation （possible foreshocks）, （3） coseismic slip, and （4） post-stress relaxation and afterslip. A sudden static stress change/perturbation in the surrounding crust can advance/ delay the fault instability or failure time and modify earth- quake rates. Based on a simple one-dimensional spring-sli- der block model with the combination of rate-and-state- dependent friction relation, in this study, we have approxi- mately derived the simple analytical solutions of clock advance/delay of fault failures caused by a sudden static Coulomb stress change applied in the different temporal evolution periods during an earthquake faulting. The results have been used in the physics-based explanation of delayed characteristic earthquake in Parkfield region, California, in which the next characteristic earthquake of M 6.0 after 1966 occurred in 2004 instead of around 1988 according to its characteristic return period of 22 years. At the same time, the analytical solutions also indicate that the time advance/ delay in Coulomb stress change derived by the dislocation model has a certain limitation and fundamental flaw. Fur- thermore, we discussed the essential difference between rate- and state-variable constitutive （R-S） model and Coulomb stress model used commonly in current earthquake triggering study, and demonstrated that, in fact, the Coulomb stress model could be involved in the R-S model. The results, we have obtained in this study, could be used in the development of time-dependent fault interaction model and the probability calculation related to the time-dependent and renewal earthquake prediction model.
基金Supported by NSFC(Grant Nos.11771044,11871007)Foundation of Anhui University of Finance and Economics(Grant No.ACKYC19051)Major Research Projects of Natural Science in Colleges and Universities of Anhui Province(Grant No.KJ2017ZD35)
文摘This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay,which is assumed to be an increasing function of the population density with lower and upper bound.Especially,state-dependent delay is introduced into a nonlocal reaction-diffusion model.The conditions of Schauder's fixed point theorem are proved by constructing a reasonable set of functionsΓ(see Section 2)and a pair of upper-lower solutions,so the existence of traveling wavefronts is established.The present study is continuation of a previous work that highlights the Laplacian diffusion.
基金Supported by NNSF of China (10901075)the Key Project of Chinese Ministry of Education (210226)+1 种基金the Scientific Research Fund of Gansu Provincial Education Department (0804-08)"Qing Lan" Talent Engineering Funds (QL-05-16A) by Lanzhou Jiaotong University
文摘This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.
