Differential Equations on Time Scales

  • Xinzhi Liu
  • Kexue Zhang
Part of the IFSR International Series in Systems Science and Systems Engineering book series (IFSR, volume 33)


This chapter focuses on differential equations on time scales, including ordinary differential equations and functional differential equations. Section 7.1 briefly introduces the theory of time scales and then fundamental theory of ordinary differential equations on time scales is presented in Section 7.2. Functional differential equations on time scales are discussed in detail in Section 7.3. First, the equation model is formulated in Subsection 7.3.1, and then basic theory about existence and uniqueness of solutions are presented in Subsection 7.3.2. In Subsections 7.3.3 and 7.3.4, various stability results are discussed, such as (uniform) stability, uniform asymptotic stability, and exponential stability. To demonstrate these results, several examples are provided in Subsection 7.3.5 along with numerical simulations.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Xinzhi Liu
    • 1
  • Kexue Zhang
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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