Abstract
We study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.
Dedicated to Professor Ivan Kiguradze on the occasion of his 80th birthday
Funding source: Universidad Complutense de Madrid
Award Identifier / Grant number: EEA
Funding source: Norges Forskningsråd
Award Identifier / Grant number: 239070
Funding statement: The work of the first author was partially supported by a EEA grant coordinated by Universidad Complutense de Madrid, Spain, and by the grant #239070 of the Norwegian Research Council.
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© 2017 by De Gruyter
Articles in the same Issue
- Frontmatter
- Strict stability with respect to initial time difference for Caputo fractional differential equations by Lyapunov functions
- Unbounded solutions for differential equations with p-Laplacian and mixed nonlinearities
- On positive periodic solutions of linear second order functional differential equations
- Existence results for nonlinear fractional Dirichlet problems on the right side of the first eigenvalue
- An existence result for multiple solutions to a Dirichlet problem
- Asymptotic analysis of positive solutions of first-order cyclic functional differential systems
- Periodic solutions of Liénard–Mathieu differential equation with a small parameter
- On a class of variational problems with nonlocal integrant
- Morse theory and multiple periodic solutions of some quasilinear difference systems with periodic nonlinearities
- The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz–Minkowski space
- Piecewise synergetic systems and applications in biochemical systems theory
- Unique solvability of the Darboux problem for linear hyperbolic functional differential equations
Articles in the same Issue
- Frontmatter
- Strict stability with respect to initial time difference for Caputo fractional differential equations by Lyapunov functions
- Unbounded solutions for differential equations with p-Laplacian and mixed nonlinearities
- On positive periodic solutions of linear second order functional differential equations
- Existence results for nonlinear fractional Dirichlet problems on the right side of the first eigenvalue
- An existence result for multiple solutions to a Dirichlet problem
- Asymptotic analysis of positive solutions of first-order cyclic functional differential systems
- Periodic solutions of Liénard–Mathieu differential equation with a small parameter
- On a class of variational problems with nonlocal integrant
- Morse theory and multiple periodic solutions of some quasilinear difference systems with periodic nonlinearities
- The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz–Minkowski space
- Piecewise synergetic systems and applications in biochemical systems theory
- Unique solvability of the Darboux problem for linear hyperbolic functional differential equations