In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol...In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.展开更多
There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain li...For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.展开更多
In this paper, we consider Lotka-Volterra predator-prey model between one and three species. Two cases are distinguished. The first is Lotka-Volterra model of one prey-three predators and the second is Lotka-Volterra ...In this paper, we consider Lotka-Volterra predator-prey model between one and three species. Two cases are distinguished. The first is Lotka-Volterra model of one prey-three predators and the second is Lotka-Volterra model of one predator-three preys. The existence conditions of nonnega-tive equilibrium points are established. The local stability analysis of the system is carried out.展开更多
We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system...We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.展开更多
In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbati...In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.展开更多
For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the...For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.展开更多
The difference equation △xn+ pnxn-k = f(n,xn-1,...,xn-1m), n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient co...The difference equation △xn+ pnxn-k = f(n,xn-1,...,xn-1m), n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient conditions for the global asymptotic stability of zero solution of the equation are obtained.展开更多
The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability ...The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.展开更多
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.展开更多
The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system ...The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.展开更多
We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their...We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.展开更多
The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature...The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).展开更多
Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m ...Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r+1/rα^r(α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.展开更多
In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^...In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS equation.With the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.展开更多
In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q...In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q d x 2 d t=x 2Q m 2x 1/Qk 2+x 1/Q-x 2.It is proved that the system is exist at least one stable periodic solution on under the following condition:m 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2】m 1δk 1(k 2+Q 2λ 2) 2.Furthermore, ifm 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2【m 1δk 1(k 2-Q 2λ 2) 2mold true them equilibrium point (s *,x * 1,x * 2)∈ set Ω is global asymptotic stable.展开更多
The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and ...The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.展开更多
Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some i...Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.展开更多
In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start wi...In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of ...The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.展开更多
文摘In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
文摘For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.
文摘In this paper, we consider Lotka-Volterra predator-prey model between one and three species. Two cases are distinguished. The first is Lotka-Volterra model of one prey-three predators and the second is Lotka-Volterra model of one predator-three preys. The existence conditions of nonnega-tive equilibrium points are established. The local stability analysis of the system is carried out.
文摘We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.
基金NUAA's Scientific Fund for the Introduction of Qualified Personnel and the National Natural Science Foundation of China(10571158).
文摘In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.
基金Project supported by the National Natural Science Foundation of China (Nos. 60274008 and 10171084)
文摘For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.
基金Supported by Natural Science Foundaton of Henan Providence(0111051200)
文摘The difference equation △xn+ pnxn-k = f(n,xn-1,...,xn-1m), n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient conditions for the global asymptotic stability of zero solution of the equation are obtained.
文摘The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
文摘The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.
文摘We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.
文摘The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).
文摘Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r+1/rα^r(α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.
基金supported by the National Science Foundation of China(Grant No.12271104,51879045)。
文摘In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS equation.With the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.
文摘In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q d x 2 d t=x 2Q m 2x 1/Qk 2+x 1/Q-x 2.It is proved that the system is exist at least one stable periodic solution on under the following condition:m 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2】m 1δk 1(k 2+Q 2λ 2) 2.Furthermore, ifm 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2【m 1δk 1(k 2-Q 2λ 2) 2mold true them equilibrium point (s *,x * 1,x * 2)∈ set Ω is global asymptotic stable.
文摘The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.
文摘Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.
文摘In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
文摘The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.