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Dynamical modelling for neural systems with direct and indirect connections is to understand how these connections contribute to neural dynamics. Despite recent findings suggesting the existence of indirect connections in neural systems, their dynamical characteristics remain poorly understood. In this paper, we propose a simplified circuit model with indirect interactions inspired by the indirect connection between two neurons, from an energy perspective. Through bifurcation and dynamics analysis, we find that the presented model has a striking resemblance with the classical Hodgkin-Huxley neuronal model. Moreover, stability in a neural network coupled with energy is demonstrated by combining stability analysis and numerical simulation. Our analysis sheds light on the excitability dynamics and multi-stability that can emerge in biophysical systems with nonlinear interactions inspired by the neural systems and highlights the role of energy in propagating electrical activities. • We construct a neuron-inspired circuit model with indirect interactions involving energy. • The neuron-like excitability and bi-stability are identified in the neuron-inspired circuit. • The neuron-inspired circuit can reproduce excitability as same bifurcation mechanism as the HH neuron. • Stability conditions of the neural network are deduced by stability analysis. • Multistability is triggered in the neural network with different coupling matrix. [ABSTRACT FROM AUTHOR]

In this paper, the memory property and the historical dynamic information of a fractional system via event-triggered control are studied. A unit step function is introduced and the control input is taken as a piecewise function. By theorem analysis and numerical simulations, it is shown that the fractional calculus of a piecewise function is relevant to the entire historical dynamic information and cannot be calculated in segments because of its memory property. So, the state of a fractional system via event-triggered control is affected by all input from the initial time, but not the triggering time, to the current time. But in previous studies, this property is neglected and the historical dynamic information has not been fully studied, which disagrees with the real physical systems. Therefore, the historical dynamic information of a fractional system via event-triggered control should be studied in order to satisfy the demands in engineering. [ABSTRACT FROM AUTHOR]

In this paper, we provide theoretical as well as numerical results concerning recurrent oscillations in Cohen-Grossberg neural networks with variable inputs and strengths of connectivity for cells, which are unpredictable or Poisson stable functions. A special case of the compartmental coefficients with periodic and unpredictable ingredients is also carefully researched. By numerical and graphical analysis, it is shown how a constructive technical characteristic, the degree of periodicity, reflects contributions of the ingredients to final outputs of the neural networks. Sufficient conditions are obtained to guarantee the existence of exponentially stable unpredictable outputs of the models. They are specified for Poisson stability by utilizing the original method of included intervals. Examples with numerical simulations that support the theoretical results are provided. [ABSTRACT FROM AUTHOR]