Algebraic Criteria for Qualitative Analysis of Nonlinear Dynamics in Biochemistry

2008 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
George Nakos
Keyword(s):  
Nonlinear Dynamics ◽  
Asymptotic Stability ◽  
Convex Hull ◽  
Qualitative Analysis ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Biochemical Reaction ◽  
Aggregate Modeling ◽  
Linear Differential Inclusions ◽  
Linear Differential

Aggregate modeling can approximate the convex hull of local matrices to nonlinear dynamics for any given accuracy. The authors use aggregate models to extend sufficient conditions for asymptotic stability of linear differential inclusions to nonlinear dynamics. An example illustrates the applicability of the proposed criteria to the analysis of nonlinear biochemical reaction chains.

scholarly journals Optimization of Lagrange problem with higher order differential inclusions and endpoint constraints

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2367-2382
Author(s):  
Elimhan Mahmudov
Keyword(s):  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Order Linear ◽  
Cost Functional ◽  
Linear Differential Inclusions ◽  
Linear Optimal Control Problems ◽  
Characteristic Features ◽  
Linear Differential ◽  
Endpoint Constraints

In the paper minimization of a Lagrange type cost functional over the feasible set of solutions of higher order differential inclusions with endpoint constraints is studied. Our aim is to derive sufficient conditions of optimality for m th-order convex and non-convex differential inclusions. The sufficient conditions of optimality containing the Euler-Lagrange and Hamiltonian type inclusions as a result of endpoint constraints are accompanied by so-called ?endpoint? conditions. Here the basic apparatus of locally adjoint mappings is suggested. An application from the calculus of variations is presented and the corresponding Euler-Poisson equation is derived. Moreover, some higher order linear optimal control problems with quadratic cost functional are considered and the corresponding Weierstrass-Pontryagin maximum principle is constructed. Also at the end of the paper some characteristic features of the obtained result are illustrated by example with second order linear differential inclusions.

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