By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established re...By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.展开更多
In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational c...In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.展开更多
It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventual...It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.展开更多
By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to ...By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.展开更多
In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.
In this paper, with the help of Lyapunov functional approach, sufficient conditions for the asymptotic stability of zero solution for a certain fourthorder non-linear delay differential equation are given.
The outbreak of coronavirus disease 2019(COVID-19)has aroused a global alert.To release social panic and guide future schedules,this article proposes a novel mathematical model,the Delay Differential Epidemic Analyzer...The outbreak of coronavirus disease 2019(COVID-19)has aroused a global alert.To release social panic and guide future schedules,this article proposes a novel mathematical model,the Delay Differential Epidemic Analyzer(D2EA),to analyze the dynamics of epidemic and forecast its future trends.Based on the traditional Susceptible-Exposed-Infectious-Recovered(SEIR)model,the D2EA model innovatively introduces a set of quarantine states and applies both ordinary differential equations and delay differential equations to describe the transition between two states.Potential variations of practical factors are further considered to reveal the true epidemic picture.In the experiment part,we use the D^2EA model to simulate the epidemic in Hubei Province.Fitting to the collected real data as non-linear optimization,the D^2EA model forecasts that the accumulated confirmed infected cases in Hubei Province will reach the peak at the end of February and then steady down.We also evaluate the effectiveness of the quarantine measures and schedule the date to reopen Hubei Province.展开更多
文摘By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.
文摘In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.
文摘It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.
基金supported by the National Natural Science Foundation of China(10461006)Basic Subject Foundation of Changzhou University(JS201004)
文摘By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.
文摘In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.
基金supported by the National Natural Science Foundation of China(No.11671227)
文摘In this paper, with the help of Lyapunov functional approach, sufficient conditions for the asymptotic stability of zero solution for a certain fourthorder non-linear delay differential equation are given.
基金the National Key Research and Development Program of China(No.2018YFB1004700)the National Natural Science Foundation of China(Nos.61872238 and 61972254)+1 种基金the Shanghai Science and Technology Fund(No.17510740200)the CCF-Huawei Database System Innovation Research Plan(No.CCF-Huawei DBIR2019002A)。
文摘The outbreak of coronavirus disease 2019(COVID-19)has aroused a global alert.To release social panic and guide future schedules,this article proposes a novel mathematical model,the Delay Differential Epidemic Analyzer(D2EA),to analyze the dynamics of epidemic and forecast its future trends.Based on the traditional Susceptible-Exposed-Infectious-Recovered(SEIR)model,the D2EA model innovatively introduces a set of quarantine states and applies both ordinary differential equations and delay differential equations to describe the transition between two states.Potential variations of practical factors are further considered to reveal the true epidemic picture.In the experiment part,we use the D^2EA model to simulate the epidemic in Hubei Province.Fitting to the collected real data as non-linear optimization,the D^2EA model forecasts that the accumulated confirmed infected cases in Hubei Province will reach the peak at the end of February and then steady down.We also evaluate the effectiveness of the quarantine measures and schedule the date to reopen Hubei Province.
