Mathematical analysis of complex biological systems using dynamical models

The mathematical modelling of biological systems with multiple components provides a systematic solution to the study of the nonlinear interactions, regulatory mechanisms and dynamic behaviours of those multiple components.The aim in this study is to build the approach of dynamical modeling using ordinary differential equations to simulate the fact of time-varying biological populations, molecular concentrations and regulatory processes.The biological assumptions and initial conditions are specified to set realistic constraints on a system, while the nonlinear interaction functions represent feedback, competition, cooperation, saturation and regulatory effects.The obtained differential equation system is analyzed by considering the equilibrium, stability analysis and numerical simulation methods.A proper numerical solution method is used to determine system trajectories for various parameter and initial conditions.The capability of the proposed model to describe steady states, transient responses, oscillatory behaviour and sensitivity to the biological parameters is also illustrated by the simulation results.