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Existence and stability of positive almost periodic solutions and periodic solutions for a Logarithmic population model

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Abstract

By means of the Cauchy matrix, we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population.

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... However, the internal changes or external disturbances in the real systems are not always periodic, but present an approximate periodic property. Almost periodicity is a kind of approximate periodicity so that mathematicians focus on the study of almost periodic systems [2,3,9,22,37,47]. For example, Xia [38] investigated the existence of almost periodic solutions of the system (3). ...
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This paper studies a delayed multispecies Logarithmic population model with feedback control. By using Krasnoselskii’s fixed point theorem and constructing Lyapunov functions, we obtain some sufficient conditions which guarantee the existence and the exponential stability of the pseudo almost periodic solutions. Meanwhile, a numerical example is also given to illustrate the feasibility of the obtained results.
... Hence, it is of great importance to consider the dynamical behaviors of logarithmic population model with almost periodically varying coefficient. Recently, by utilizing the continuation theorem and contraction mapping principle, some criteria have been established to prove the existence and local exponential stability of positive almost periodic solutions for delay logarithmic population model and its generalized modification in the literature; see [13][14][15][16][17]. However, to the best of our knowledge, there is no literature considering the existence and global exponential stability of positive almost periodic solutions problem for delay logarithmic population model. ...
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... For this reason, the assumption of almost periodicity is more realistic, more important, and more general when we consider the effects of the environmental factors. In fact, there have been many nice works on the positive almost periodic solutions of continuous and discrete dynamics model with almost periodic coefficients (see [7,12,13,[22][23][24][25][26][27][28] and the references cited therein). ...
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... Thus, the investigation of almost periodic behavior is considered to be more accordant with reality. Although it has widespread applications in real life, the generalization to the notion of almost periodicity is not as developed as that of periodic solutions; we refer the reader to [13][14][15][16][17][18][19][20][21][22][23][24]. ...
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