Dynamics of a neuron exposed to integer-and fractional-order discontinuous external magnetic flux

We propose a modified Fitzhugh-Nagumo neuron(MFNN) model. Based on this model, an integerorder MFNN system(case A) and a fractional-order MFNN system(case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractionalorder magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.

上位效应对遗传算法可靠性的影响（英文）

目的:探讨遗传算法的局限性和实用性,并分析基于相互作用产生的上位效应对遗传算法可靠性的影响。创新点:1.指出遗传算法缺陷的根源;2.基于测试样本函数定义目标函数,以判断遗传算法的适用性。方法:1.基于非上位效应函数(表1)和上位效应函数(表2),以及非上位效应函数F4和上位效应函数F6的结构图来验证遗传算法可靠性;2.通过计算样本函数(公式(1))和遗传算法流程(图3)表达遗传算法的工作原理。3.利用克洛弗函数(公式(2))和计算不同结构角下的函数分布(图4),进一步判断匹配度(表3)和计算效率(表4);定义新的目标函数(公式(9))和一组新的变量(公式(10))来实现变量相关性解离。结论:1.对当前遗传算法存在的不足给出了独到见解,并认为正定性的假设并非可以保证遗传算法实际的有效性和优化性。2.定义成本代价函数用以判断遗传算法可靠性,并分别考虑上位性和非上位性效应两种情形。当成本代价函数在非上位性效应下时,遗传算法是有效的;否则,可以把N维函数降级为N个一维函数,从而采用更简单的算法来判断。基于一些通用的基准,进一步设计三类样本函数来证实以上判断,且这些样本函数适合于上位性效应情形和非上位效应情形。3.遗传算法的瓶颈在于主算子和相干匹配性;可以通过破坏某些结构来实现变量关系的解离,从而抑制相干匹配性对遗传算法的影响。希望相关读者在处理实际优化问题时能验证作者关于上位效应的定性结论,并给出更可靠的方法来表征这种效应。