From Duffing Equation to Bio-oscillations

2023
Felix Sadyrbaev, Inna Samuilika

We consider systems of ordinary differential equations, arising in applications. The focus is on attractors and their properties. Since attractors determine the evolution of systems and the behavior of their solutions, this information is necessary to monitor and manage the networks that are modeled by these systems. Particular attention is paid to the types of attractors, including chaotic ones. Three classes of systems are considered. The first is the occurrence of chaos in a certain system which is a generalization of the Duffing equation is analyzed. Then, the three- and four-dimensional systems, arising in the theory of gene regulatory networks, are studied. Examples of systems, which have attractors of different types, are given. A significant part of the chapter is devoted to four-, five-, and six-dimensional systems found in the theory of neuronal networks. Here, the hyperbolic tangent is chosen as the activating function. Several examples of chaotic behavior of solutions are given. The presentation is accompanied by multiple illustrations.

Keywords
Gene regulatory networks Neuronal networks Dynamical systems Attractors Phase space Bio-oscillations Duffing equation Chaotic behavior Lyapunov exponents
DOI
10.1007/978-3-031-42689-6_7
Hyperlink
https://link.springer.com/chapter/10.1007/978-3-031-42689-6_7

Sadyrbaev, F., Samuilika, I. From Duffing Equation to Bio-oscillations. In: Computational and Mathematical Models in Biology. Nonlinear Systems and Complexity. Vol.38. Cham: Springer, 2023. pp.159-182. ISBN 978-3-031-42688-9. e-ISBN 978-3-031-42689-6. Available from: doi:10.1007/978-3-031-42689-6_7

Publication language
English (en)