A Bifurcation of Solutions of Nonlinear Fredholm Inclusions Involving CJ-Multimaps with Applications to Feedback Control Systems

作者：Nguyen Van Loi; Obukhovskii, Valeri; Yao, Jen Chih^*

来源：Set-Valued and Variational Analysis, 2013, 21(2): 247-269.

DOI：10.1007/s11228-012-0226-z

• Bifurcation
• Nonlinear Fredholm operator
• CJ-multimap
• Oriented coincidence index
• Guiding function
• Feedback control system
• Differential inclusion
• Periodic solution

In this paper, by applying the oriented coincidence index for a pair consisting of a nonlinear Fredholm operator and a CJ-multimap, we prove a global bifurcation theorem for solutions of families of inclusions with such maps. The method of guiding functions is used to calculate the oriented coincidence index for a class of feedback control systems. This characteristic allows to obtain the existence result for periodic trajectories of such systems. From the other side, it opens the possibility to apply the abstract bifurcation result to the study of qualitative behavior of branches of periodic trajectories.

• 出版日期2013-6
• 单位中山大学