Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections,Rates and Inputs

In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.     

Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations

In this paper, modulo periodic Poisson stable functions have been newly introduced. Quasilinear differential equations with modulo periodic Poisson stable coefficients are under investigation. The existence and uniqueness of asymptotically stable modulo periodic Poisson stable solutions have been proved. Numerical simulations, which illustrate the theoretical results are provided.     

Synthesis of porous C/Fe3O4 microspheres by spray pyrolysis with NaNO3 additive for lithium-ion battery applications

In this work, we successfully synthesized porous C/Fe₃O₄ microspheres by spray pyrolysis at 700ºC with a sodium nitrate (NaNO₃) additive in the precursor solution. Furthermore, we studied their electrochemical properties as anode material for Li-ion batteries. The systematic studies by various characterization techniques show that NaNO₃ catalyzes the carbonization of sucrose and enhances the crystallization of Fe₃O₄. Moreover, an aqueous etching can easily remove sodium compounds to produce porous C/Fe₃O₄ microspheres with large surface areas and pore volumes. The porous C/Fe₃O₄ microspheres exhibit a reversible capacity of ~780 mAh g^–1 in the initial cycles and ~520 mAh g^–1 after 30 cycles at a current density of 50 mA g^–1. Moreover, a reversible capacity of ~400 mAh g^–1 is attainable after 200 cycles, even at a high current density of 500 mA g^–1. The wide range of pores produced from the removal of sodium compounds might enable easy electrolyte penetration and facilitate fast Li-ion diffusion, while the N-doping can promote the electronic conductivity of the carbon. These features of porous C/Fe₃O₄ microspheres led to the improved electrochemical properties of this sample.

Graphical Abstract