2.3.1 Mechanistic Models
The development of a mechanistic mathematical model requires sufficient
understanding of the physical, chemical, and biological processes that occur in a
system and its use demands a proper validation. These kind of models are
explanatory models, and they can be static or dynamic (Kita 2011). In addition, the
study and description of a system involves two processes construction of mathematical models and numerical solution of the set of equations that describe the
behavior of the system, through the use of a digital computer.
Mechanistic models are based on the assumption that the state of a system can
be quantified and that changes in the state can be described by mathematical
equations, equations of rate of change or differential equations. These models
include several components: state variables, differential equations, parameters, and
inputs. Normally, a state variable is a variable that appears in the accumulation
term of adynamic balance of mass or energy. A state variable is a variable that can
be quantified (at least conceptually) and it allows knowing the behavior of the
system at all future instant in time (Kita 2011).
2.3.1.1 Modeling Phases
There are three phases in the process of the mathematical modeling (Ljung and
Glad 1994):
1. The problem is structured.
2. The basic equations are formulated.
3. The state-space model is formed.
If the model is not too complex in terms of state variables, it can be used to
design control systems for example optimal control strategies (Seginer and
Ioslovich 1998; Van Henten 1994; Tap 2000) for the best growth, production,
and crop quality.
The problem is structured
It is important to understand the general structure of the system (Ljung and Glad
1994). Thus, we need to answer the following questions:
• What signals are outputs and inputs?
• What happen in the system?
• What quantities are constants?
• What signals are internal variables?
When we have decided what variables in the systems are of interest and how
they interact, then we attempt to divide the system into subsystems. This phase
puts the great demands on the modeler because it requires the understanding of the
2 Mathematical Modeling of Biosystems
57
The development of a mechanistic mathematical model requires sufficient
understanding of the physical, chemical, and biological processes that occur in a
system and its use demands a proper validation. These kind of models are
explanatory models, and they can be static or dynamic (Kita 2011). In addition, the
study and description of a system involves two processes construction of mathematical models and numerical solution of the set of equations that describe the
behavior of the system, through the use of a digital computer.
Mechanistic models are based on the assumption that the state of a system can
be quantified and that changes in the state can be described by mathematical
equations, equations of rate of change or differential equations. These models
include several components: state variables, differential equations, parameters, and
inputs. Normally, a state variable is a variable that appears in the accumulation
term of adynamic balance of mass or energy. A state variable is a variable that can
be quantified (at least conceptually) and it allows knowing the behavior of the
system at all future instant in time (Kita 2011).
2.3.1.1 Modeling Phases
There are three phases in the process of the mathematical modeling (Ljung and
Glad 1994):
1. The problem is structured.
2. The basic equations are formulated.
3. The state-space model is formed.
If the model is not too complex in terms of state variables, it can be used to
design control systems for example optimal control strategies (Seginer and
Ioslovich 1998; Van Henten 1994; Tap 2000) for the best growth, production,
and crop quality.
The problem is structured
It is important to understand the general structure of the system (Ljung and Glad
1994). Thus, we need to answer the following questions:
• What signals are outputs and inputs?
• What happen in the system?
• What quantities are constants?
• What signals are internal variables?
When we have decided what variables in the systems are of interest and how
they interact, then we attempt to divide the system into subsystems. This phase
puts the great demands on the modeler because it requires the understanding of the
2 Mathematical Modeling of Biosystems
57