电磁驱动下一类混合神经元模型的动力学响应与图像加密应用  

Dynamic Response of a Class of Hybrid Neuron Model by Electromagnetic Induction and Application of Image Encryption

作　　者：安新磊[1,2] 熊丽 乔帅[4] AN Xinlei;XIONG Li;QIAO Shuai(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China;College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China;School of Physics and Electromechanical Engineering,Hexi University,Zhangye 734000,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070 [2]兰州理工大学电气工程与信息工程学院,兰州730050 [3]河西学院物理与机电工程学院,张掖734000 [4]西北师范大学数学与统计学院,兰州730070

出　　处：《电子与信息学报》2023年第3期929-940,共12页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(11962012,62061014)。

摘　　要：在神经元活动的模型建立和分析过程中,应考虑一些生物物理效应。由于神经系统内部细胞内外离子浓度的波动,在集体电活动和神经元集群之间信号传播的过程中需要考虑电磁场的内部波动和跨膜磁通的影响。该文在一类混合神经元中引入磁通变量,通过对膜电位的调制诱发复杂的时变电磁场,运用Xppauto,Matcont和MATLAB等分析工具,探讨了新模型平衡点的存在性、初值敏感性和双参数分岔,发现外界刺激电流和电磁场变化时,可诱发新模型产生丰富的放电模式,如静息态、尖峰放电、周期(或混沌)簇放电,特别是由于磁通变量及忆阻器的引入产生的共存放电、隐藏放电等新现象。通过上述分析,基于电磁感应的神经元模型具有高非线性和较多的敏感参数,可使加密算法具有较大的密钥空间,基于此,该文设计了一种图像加密算法,对明文图像的像素先进行1次扩散再对其位置进行两次置乱。最后,通过一系列数值实验证明所设计的加密算法能有效地加密图像并且具有较高的安全性。该文考虑了神经细胞内外的电磁感应效应,有助于更全面了解神经元之间的信息编码和转迁规律,更多的分岔参数和高复杂性也使所设计的神经元模型在图像加密中具有很好的应用前景。During the modeling and analysis of neuronal activity,several biophysical effects should be taken into consideration.Due to fluctuations in intracellular and extracellular ion concentrations within the nervous system,internal fluctuations of electromagnetic fields and the effects of transmembrane magnetic flux need to be considered in the collective electrical activity and signal propagation between neuronal clusters.In this paper,a magnetic flux variable is introduced into a hybrid neuron,and a complex time-varying electromagnetic field is induced by modulating the membrane potential.Using analytical tools such as Xppauto,Matcont and Matlab,the existence and initial value of the equilibrium point of the new model,sensitivity and two-parameter bifurcation are discussed.When the external stimulus current and electromagnetic field change,the new model can be induced to generate abundant discharge modes,such as resting state,spike discharge,periodic(or chaotic)cluster discharge,especially coexisting discharge and hidden discharge benefited from the introduction of magnetic flux variable and memristor.According to the above analysis,the neuron model based on electromagnetic induction has high nonlinearity and more sensitive parameters,which enables the encryption algorithm to have a large key space.Based on this,an image encryption algorithm is designed in this paper.Pixels are first diffused once and then scrambled twice to their positions.Finally,through a series of numerical experiments,it is proved that the designed encryption algorithm can encrypt images effectively and has high security.The research takes into account the electromagnetic induction effect inside and outside the nerve cells,which is helpful for a more comprehensive understanding of the information encoding and transition laws between neurons.More bifurcation parameters and high complexity also make the designed neuron model has a good application prospect in image encryption.

关 键 词：混合神经元模型 电磁感应 双参数分岔 共存放电 图像加密 

分 类 号：O441[理学—电磁学] TN918.4[理学—物理]