In this paper, a class of survival red blood cells model with time-varying delays and impulsive effects is considered. First, some sufficient conditions for the persistence are derived by use of the theory on impulsive differential equations. The persistence describes the persistent survival of the mature red blood cells in the mammal under delay and impulsive perturbations. Then assuming that the coefficients in the model are $\omega$-periodic, some criteria ensuring the existence-uniqueness and global attractivity of positive $\omega$-periodic solution of the addressed model are obtained, which are suitable for survival red blood cells model with any $\omega \in {\mathbb{R}}_{+}$. These global attractivity criteria describe the nonexistence of any dynamic diseases in the mammal. Moreover, our proposed results in this paper extend and improve some recent works in the literature. Finally, two examples and their computer simulations are given to show the effectiveness and advantages of the results.

Interneurons modulate the excitability of neural networks and maintain neural activity balance via inhibitory or excitatory synaptic connections. Here, we studied the formation of patterns of interneuronal networks with inhibitory synaptic coupling. We found that both electrical synaptic coupling and inhibitory synaptic coupling play a crucial role in the formation of neural network patterns. In addition, delayed inhibitory synapses can also affect the transition of target waves to chaotic states. As the strength of electrical synaptic coupling increases, the firing behavior of neurons gradually becomes highly ordered. When the inhibitory synaptic delay reaches a critical value, we observe a transition in oscillatory patterns from an ordered state to a synchronized state. We further investigated how inhibitory synaptic conductance influences the formation of oscillatory patterns in the network. The study reveals that increasing synaptic conductance disrupts the structure of target waves, inducing chaotic states such as spiral wave fragmentation, while simultaneously elevating neuronal firing rates.