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Cell membrane of biological neurons has distinct geometric structure, and involvement of diffusive term is suitable to estimate the spatial effect of cell membrane on neural activities. The gradient field diversity between two sides of the cell membrane can be approached by using a double-layer membrane model for the neuron. Therefore, two capacitive variables and diffusive terms are used to investigate the neural activities of cell membrane, and the local kinetics is described by a functional circuit composed of two capacitors. The voltages for the two parallel capacitors describe the inner and outer membrane potentials, and the diffusive effect of ions is considered on the membrane surface. The results reveal that neural activities are relative to the capacitance ratio between the inside and outside of the membrane and diffusive coefficient. High-energy periodic external stimulation induces the target waves to spread uniformly, while low-energy chaotic stimulation results in wave fragmentation. Furthermore, when the capacitance ratio exhibits exponential growth under an adaptive control law, the resulting energy gradient within the network induces stable target waves. That is, energy distribution affects the wave propagation and pattern formation in the neuron. The result indicates that the spatial diffusive effect and capacitance diversity between outer and inner cell membranes are important for selection of firing patterns and signal processing during neural activities. This model is more suitable to estimate neural activities than using generic oscillator-like or map neurons without considering the spatial diffusive effect.
Cell membrane of biological neurons has distinct geometric structure, and involvement of diffusive term is suitable to estimate the spatial effect of cell membrane on neural activities. The gradient field diversity between two sides of the cell membrane can be approached by using a double-layer membrane model for the neuron. Therefore, two capacitive variables and diffusive terms are used to investigate the neural activities of cell membrane, and the local kinetics is described by a functional circuit composed of two capacitors. The voltages for the two parallel capacitors describe the inner and outer membrane potentials, and the diffusive effect of ions is considered on the membrane surface. The results reveal that neural activities are relative to the capacitance ratio between the inside and outside of the membrane and diffusive coefficient. High-energy periodic external stimulation induces the target waves to spread uniformly, while low-energy chaotic stimulation results in wave fragmentation. Furthermore, when the capacitance ratio exhibits exponential growth under an adaptive control law, the resulting energy gradient within the network induces stable target waves. That is, energy distribution affects the wave propagation and pattern formation in the neuron. The result indicates that the spatial diffusive effect and capacitance diversity between outer and inner cell membranes are important for selection of firing patterns and signal processing during neural activities. This model is more suitable to estimate neural activities than using generic oscillator-like or map neurons without considering the spatial diffusive effect.
The bipolar pulse current can effectively mimic the external time-varying stimulus of neurons, and its effect of neuronal dynamics has rarely been reported. To this end, this paper reports the effects of bipolar pulses on a two-dimensional single inertial neuron model, showcasing the chaotic dynamics of hidden attractors and coexisting symmetric attractors, which is of significant importance for understanding the complex behaviors of neuron dynamics under time-varying external stimuli and its application. Firstly, the mathematical model of the single intertial neuron model with forced bipolar pulse is presented, and then the equilibrium states behaving as unstable saddle point (USP), stable node-focus (SNF), and stable node point (SNP) are analyzed. Additionally, by using multiple dynamical methods including bifurcation plots, basins of attraction, and phase plots, complex dynamics of interesting bifurcation behaviors and coexisting attractors are revealed, which are induced by the forced bipolar pulse current as well as initial values, both. In addition, such effets are well valideted via a simple multiplerless electronic neuron circuit. The implementation circuit of presented model is constructed on the analog level and executed using PSIM circuit platform. The measurement results verified the double-scroll chaotic attractors and the coexisting period/chaos behaviors. Finally, the chaotic sequences of the model are applied to color image encryption for the benefit of requirements on modern security field. The encryption effectiveness is demonstrated through various evaluation indexes, including histogram analysis, information entropy, correlation coefficient, plaintext sensitivity, and resistance to noise attacks.
The symmetric multi-scroll strange attractor has shown great potential in chaos-based applications due to its high complexity in phase space. Here, the approach of symmetrization is employed for attractor doubling to generate pseudo-multi-scroll attractors in a discrete map, where a carefully selected offset constant is the key to organizing coexisting attractors. By choosing the Hénon map to generate the pseudo-multi-scroll attractor and implementing the digital circuit on a microcontroller, this study fills a significant gap in the research on discrete chaotic systems. The complexity performance is further validated using a pseudo-random number generator, demonstrating substantial academic contributions to the field of chaos theory. Additionally, a pseudo-multi-scroll attractor-based squirrel search algorithm is first developed, showcasing its practical application in mobile robot path planning. This work not only advances the theoretical understanding of chaotic systems but also provides practical methods for implementation in digital systems, offering valuable insights for policy-making in advanced robotic systems and intelligent manufacturing.
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