• 대한수학회지
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• 제50권6호
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• pp.1165-1181
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• 2013

In this paper, we consider a class of periodic It$\hat{o}$ stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the results obtained by It$\hat{o}$ et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al. [7].

• 충청수학회지
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• 제20권4호
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• pp.449-455
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• 2007

We obtain a discrete version of a fundamental result by Yoshizawa related to the existence of almost periodic solutions of functional differential equations with finite delay.

• 충청수학회지
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• 제23권2호
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• pp.401-409
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• 2010

We study the existence of periodic solutions of Volterra equations by using the limiting equations and contraction mappings.

• 대한수학회지
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• 제48권2호
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• 대한수학회지
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• 제41권4호
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• pp.747-754
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• 2004

In this paper we investigate the existence and uniqueness of almost periodic and pseudo almost periodic solution for nonlinear differential equation with reflection of argument. For the case of almost periodic forced term, we consider the frequency modules of the solutions.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.577-594
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• 2013

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

• 대한수학회보
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• 제32권2호
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• pp.271-279
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• 1995

In 1986, Fabry, Mawhin and Nkashama [1] have considered periodic solutios for Lienard equation $$ (1_s) x" + f(x)x' + g(t,x) = s, $$ where s is a real parameter, f and g are continuous functions, and g is $2\pi$-periodic in t and have proved that if $$ (H) lim_{$\mid$x$\mid$\to\infty} g(t,x) = \infty uniformly in t \in [0,2\pi], $$ there exists $s_1 \in R$ such that $(1_s)$ has no $2\pi$periodic solution if $s< s_1$, and at least one $2\pi$-periodic solution if $s = s_1$, and at least two $2\pi$-periodic solutions if $s > s_1$.s_1$.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.639-651
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• 2009

In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.

• 대한수학회논문집
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• 제33권3호
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• pp.1039-1048
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• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.29-44
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• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.