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This is an introductory paper of the Focus Issue Recent advances in modeling complex systems: Theory and applications, where papers presenting new advances and insights into chaotic dynamics, fractional dynamics, complex oscillations, complex traffic dynamics, and complex networks, as well as their applications, are collected. All these different problems share common ideas and methods and provide new perspectives for further progress in the modeling of complex systems. [ABSTRACT FROM AUTHOR]

Circuit implementation of the mathematical model of neurons represents an alternative approach for the validation of their dynamical behaviors for their potential applications in neuromorphic engineering. In this work, an improved FitzHugh–Rinzel neuron, in which the traditional cubic nonlinearity is swapped with a sine hyperbolic function, is introduced. This model has the advantage that it is multiplier-less since the nonlinear component is just implemented with two diodes in anti-parallel. The stability of the proposed model revealed that it has both stable and unstable nodes around its fixed points. Based on the Helmholtz theorem, a Hamilton function that enables the estimation of the energy released during the various modes of electrical activity is derived. Furthermore, numerical computation of the dynamic behavior of the model revealed that it was able to experience coherent and incoherent states involving both bursting and spiking. In addition, the simultaneous appearance of two different types of electric activity for the same neuron parameters is also recorded by just varying the initial states of the proposed model. Finally, the obtained results are validated using the designed electronic neural circuit, which has been analyzed in the Pspice simulation environment. [ABSTRACT FROM AUTHOR]

The phenomenon of hidden heterogeneous extreme multistability is rarely reported in coupled neurons. This phenomenon is investigated in this contribution using a model of a 2D FitzHugh–Nagumo neuron coupled with a 3D Hindmarsh–Rose neuron through a multistable memristive synapse. The investigation of the equilibria revealed that the coupled neuron model is equilibrium free and, thus, displays a hidden dynamics. Some traditional nonlinear analysis tools are used to demonstrate that the heterogeneous neuron system is able to exhibit the coexistence of an infinite number of electrical activities involving both periodic and chaotic patterns. Of particular interest, a noninvasive control method is applied to suppress all the periodic coexisting activities, while preserving only the desired chaotic one. Finally, an electronic circuit of the coupled neurons is designed in the PSpice environment and used to further support some results of the theoretical investigations. [ABSTRACT FROM AUTHOR]