Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 11

time scales Related Publications

11 Nonoscillation Criteria for Nonlinear Delay Dynamic Systems on Time Scales

Authors: Xinli Zhang

Abstract:

In this paper, we consider the nonlinear delay dynamic system xΔ(t) = p(t)f1(y(t)), yΔ(t) = −q(t)f2(x(t − τ )). We obtain some necessary and sufficient conditions for the existence of nonoscillatory solutions with special asymptotic properties of the system. We generalize the known results in the literature. One example is given to illustrate the results.

Keywords: time scales, Dynamic System, oscillation, two-dimensional

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10 Periodic Solutions for a Food Chain System with Monod–Haldane Functional Response on Time Scales

Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.

Keywords: time scales, periodic solution, coincidence degree, Food chain system

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9 Partial Derivatives and Optimization Problem on Time Scales

Authors: Francisco Miranda

Abstract:

The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here.

Keywords: Mathematical Programming, time scales, optimization problem, Lagrange multipliers

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8 Periodic Solutions for a Two-prey One-predator System on Time Scales

Authors: Changjin Xu

Abstract:

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

Keywords: time scales, periodic solution, coincidence degree, competitive system, topological degree

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7 Periodic Solutions of Recurrent Neural Networks with Distributed Delays and Impulses on Time Scales

Authors: Yongkun Li, Yaping Ren

Abstract:

In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.

Keywords: time scales, Recurrent Neural Networks, Periodic solutions, Global exponential stability, impulses, distributed delays

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6 Periodic Solutions in a Delayed Competitive System with the Effect of Toxic Substances on Time Scales

Authors: Qianhong Zhang, Changjin Xu

Abstract:

In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.

Keywords: time scales, periodic solution, coincidence degree, competitive system, topological degree

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5 Periodic Solutions for a Delayed Population Model on Time Scales

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

Keywords: time scales, Periodic solutions, coincidence degree, continuation theorem

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4 Existence of Periodic Solutions in a Food Chain Model with Holling–type II Functional Response

Authors: Zhaohui Wen

Abstract:

In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin-s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: time scales, Periodic solutions, food chain model, coincidence degree

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3 Periodicity for a Semi–Ratio–Dependent Predator–Prey System with Delays on Time Scales

Authors: Kejun Zhuang

Abstract:

In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: time scales, coincidence degree, Semi–ratio–dependent, predator–prey system

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2 Existence and Stability of Anti-periodic Solutions for an Impulsive Cohen-Grossberg SICNNs on Time Scales

Authors: Meng Hu, Lili Wang

Abstract:

By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of antiperiodic solutions for a kind of impulsive Cohen-Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate our results.

Keywords: time scales, impulse, coincidence degree, Anti-periodic solution, CGSICNNs

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1 Periodicity for a Food Chain Model with Functional Responses on Time Scales

Authors: Kejun Zhuang

Abstract:

With the help of coincidence degree theory, sufficient conditions for existence of periodic solutions for a food chain model with functional responses on time scales are established.

Keywords: time scales, Periodic solutions, food chain model, coincidence degree

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