A nonlinear hyperbolic system modeling currency hoarding

  • Suman Kumar TumuluriEmail author
  • A. S. Vasudeva Murthy
Original Paper


We present a nonlinear model for replacement, regulation of currency in circulation and hoarding currency. The nonlinearity enters the model in the regulatory term which depends on the total currency in the circulation. We provide an existence and uniqueness result for the model as well as its steady state. Local and global dynamics of the solution is studied for large time. In fact, convergence of the solution to the nontrivial steady state is obtained in both the linearized and nonlinear cases. Furthermore, we have analyzed the dynamics of the total currency in circulation and hoarding for large time by constructing a Lyapunov function. Convergence of the total currency in circulation and hoarding to the steady state is established using this Lyapunov function.


Renewal equations Linear stability Global stability Lyapunov function 

Mathematics Subject Classification

35Q91 91B55 



The authors are grateful to the anonymous reviewer for his/her valuable suggestions and comments which greatly improved the quality of the manuscript. This work was completed while the the first author was visiting TIFR-CAM, Bangalore and he would like to express his gratitude for the hospitality extended to him there. The first author is supported by UGC–SAP DSA 1.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of HyderabadHyderabadIndia
  2. 2.TIFR-CAMBangaloreIndia

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