In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equat...In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations using Newton iteration method. We give numerical results to satisfy the accuracy and the applicability of the proposed schemes.展开更多
A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system.In the process of generating a key stream,the time-varying delay and fractional derivative are embedded in the prop...A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system.In the process of generating a key stream,the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security.Such a scheme is described in detail with security analyses including correlation analysis,information entropy analysis,run statistic analysis,mean-variance gray value analysis,and key sensitivity analysis.Experimental results show that the newly proposed image encryption scheme possesses high security.展开更多
This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real n...This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.展开更多
A non-autonomous Logistic type equation with infinite delay is investigated. For general nonautonomous case, sufficient conditions which guarantee the uniform persistence and globally attractivity of the system arc ob...A non-autonomous Logistic type equation with infinite delay is investigated. For general nonautonomous case, sufficient conditions which guarantee the uniform persistence and globally attractivity of the system arc obtained; For almost periodic case, by means of a suitable Lyapunov functional, sufficient conditions are derived for the existence and uniqueness of almost periodic solution of the system. Some new results are obtained.展开更多
Sufficient conditions are presented for the asymptotic behavior of all positive solutions of the multiplicative delay Logistic equation about the positive equilibrium K. The case when r(t) =r and gj(t) = t - Tj or gj(...Sufficient conditions are presented for the asymptotic behavior of all positive solutions of the multiplicative delay Logistic equation about the positive equilibrium K. The case when r(t) =r and gj(t) = t - Tj or gj(t) = [t - kj], [.] denoting the greatest integer function,where r, Tj and kj are positive constants, j = 1, 2,... m, ale also included.展开更多
The existence and the global attractivity of a positive periodic solution of the delay differential equation y·(t)=y(t)F[t, y(t-τ 1(t)),...,y(t-τ n(t))] are studied by using some techniques of the Mawhin coinci...The existence and the global attractivity of a positive periodic solution of the delay differential equation y·(t)=y(t)F[t, y(t-τ 1(t)),...,y(t-τ n(t))] are studied by using some techniques of the Mawhin coincidence degree theory and the constructing suitable Liapunov functionals. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved.展开更多
The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-ma...The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-mathematics models, some conjectures and open problems appearing in literature are solved, and many known results are improved.展开更多
文摘In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations using Newton iteration method. We give numerical results to satisfy the accuracy and the applicability of the proposed schemes.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61004078 and 60971022)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2009GQ009 and ZR2009GM005)+1 种基金the China Postdoctoral Science Foundationthe Special Funds for Postdoctoral Innovative Projects of Shandong Province,China
文摘A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system.In the process of generating a key stream,the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security.Such a scheme is described in detail with security analyses including correlation analysis,information entropy analysis,run statistic analysis,mean-variance gray value analysis,and key sensitivity analysis.Experimental results show that the newly proposed image encryption scheme possesses high security.
文摘This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.
基金Supported by the National Natural Science Foundation of China(10501007)the Foundation of Science and Technology of Fujian Province for Young Scholars(2004J0002)Foundation of Fujian Education Bureau(JA04156).
文摘A non-autonomous Logistic type equation with infinite delay is investigated. For general nonautonomous case, sufficient conditions which guarantee the uniform persistence and globally attractivity of the system arc obtained; For almost periodic case, by means of a suitable Lyapunov functional, sufficient conditions are derived for the existence and uniqueness of almost periodic solution of the system. Some new results are obtained.
文摘Sufficient conditions are presented for the asymptotic behavior of all positive solutions of the multiplicative delay Logistic equation about the positive equilibrium K. The case when r(t) =r and gj(t) = t - Tj or gj(t) = [t - kj], [.] denoting the greatest integer function,where r, Tj and kj are positive constants, j = 1, 2,... m, ale also included.
文摘The existence and the global attractivity of a positive periodic solution of the delay differential equation y·(t)=y(t)F[t, y(t-τ 1(t)),...,y(t-τ n(t))] are studied by using some techniques of the Mawhin coincidence degree theory and the constructing suitable Liapunov functionals. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved.
基金Project partially supported by the National Nature Science Foundation of Chinathe Natural Scienee Foundation of Hunan Province.
文摘The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-mathematics models, some conjectures and open problems appearing in literature are solved, and many known results are improved.