This paper is concerned with boundary value problems for systems of nonlinear second-order differential equations. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.

This paper is concerned with a stochastic ratio-dependent predator-prey model with varible coefficients. By the comparison theorem of stochastic equations and the Itô formula, the global existence of a unique positive solution of the ratio-dependent model is obtained. Besides, some results are established such as the stochastically ultimate boundedness and stochastic permanence for this model.

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue ofV-function technique,M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

Background Orphan gene play an important role in the environmental stresses of many species and their identification is a critical step to understand biological functions. Moso bamboo has high ecological, economic and cultural value. Studies have shown that the growth of moso bamboo is influenced by various stresses. Several traditional methods are time-consuming and inefficient. Hence, the development of efficient and high-accuracy computational methods for predicting orphan genes is of great significance. Results In this paper, we propose a novel deep learning model (CNN + Transformer) for identifying orphan genes in moso bamboo. It uses a convolutional neural network in combination with a transformer neural network to capture k-mer amino acids and features between k-mer amino acids in protein sequences. The experimental results show that the average balance accuracy value of CNN + Transformer on moso bamboo dataset can reach 0.875, and the average Matthews Correlation Coefficient (MCC) value can reach 0.471. For the same testing set, the Balance Accuracy (BA), Geometric Mean (GM), Bookmaker Informedness (BM), and MCC values of the recurrent neural network, long short-term memory, gated recurrent unit, and transformer models are all lower than those of CNN + Transformer, which indicated that the model has the extensive ability for OG identification in moso bamboo. Conclusions CNN + Transformer model is feasible and obtains the credible predictive results. It may also provide valuable references for other related research. As our knowledge, this is the first model to adopt the deep learning techniques for identifying orphan genes in plants.

By using the Lyapunov functions and the Razumikhin techniques, the exponential stability of impulsive functional differential systems with delayed impulses is investigated. The obtained results have shown that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and they improve and complement ones from some recent works. An example is provided to illustrate the effectiveness and the advantages of the results obtained.

Periodic neutral functional differential equations are considered. Sufficient conditions for existence, uniqueness and global attractivity of periodic solutions are established by combining the theory of monotone semiflows generated by neutral functional differential equations and Krasnosel'skii's fixedpoint theorem. These results are applied to a concrete neutral functional differential equation that can model single-species growth, the spread of epidemics, and the dynamics of capital stocks in a periodic environment.

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This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Finally, an example is given to illustrate the main results.