Setting the Stage: Complex Systems, Emergence and Evolution
7
to model behavior of water in pipes. Using these equations can represent the
system as a derivative of time [144],
˙
X =
dx
dt
= F (x)
(1.1)
Equation 1.1 shows change in a system represented with time, where X =
(x
(1) , x
(2) , ..., x
(k) ) and k is the number of states of the system. The system
state is given as a property (for all elements) as a snapshot at the time. This
can include individual element properties, environmental conditions and any
other attributes involved. Basically, it is a snapshot of the system at time t,
taken between starting time t = 0 and time t = k. In this way, it is possible to
determine how the system looks at time t = t + 1, if state at t = t is known.
However, complex systems are emergent systems. This makes it sometimes
difficult to predict or anticipate, how the system would look at t + 1 as there
are too many individual element interactions leading to its snapshot at t + 1
due to randomness in individual behavior. These systems are also irreversible,
which means it is also difficult to work backwards and deduce what the past
state was even if current and future states are known. Researchers can deduce
a number of reasons why the system behaved in the way, by running repeated
simulations and testing the effect of all elements on overall system behavior.
1.6 Is There Evolution at Work?
Being continually adaptive, systems show continuous dynamic change.
This uses fewer or basic starting conditions and assumptions to grow into
complex system behavior. As time moves forward, certain conditions can be
changed to alter its behavior and future system states. Other components that
play a key role include geography or locations in the system. Geography can
influence in ways such as the following:
Communication span for each individual. Messages or communication
between individuals, which are limited to particular individuals in an
area. This gives them more information and act accordingly.
Messages influence personal behavior. Received messages can be used
to determine the next strategies to play based on the incoming information.
Influence of resource availability. Depending on their locations, each individual has various levels of resource available, that can affect its behavior. For example, in a ant colony model, if an ant comes across a stream
of water, it can locally change its on-course path, effectively adapting to
the situation and locality. Over time, the system will display a stronger
7
to model behavior of water in pipes. Using these equations can represent the
system as a derivative of time [144],
˙
X =
dx
dt
= F (x)
(1.1)
Equation 1.1 shows change in a system represented with time, where X =
(x
(1) , x
(2) , ..., x
(k) ) and k is the number of states of the system. The system
state is given as a property (for all elements) as a snapshot at the time. This
can include individual element properties, environmental conditions and any
other attributes involved. Basically, it is a snapshot of the system at time t,
taken between starting time t = 0 and time t = k. In this way, it is possible to
determine how the system looks at time t = t + 1, if state at t = t is known.
However, complex systems are emergent systems. This makes it sometimes
difficult to predict or anticipate, how the system would look at t + 1 as there
are too many individual element interactions leading to its snapshot at t + 1
due to randomness in individual behavior. These systems are also irreversible,
which means it is also difficult to work backwards and deduce what the past
state was even if current and future states are known. Researchers can deduce
a number of reasons why the system behaved in the way, by running repeated
simulations and testing the effect of all elements on overall system behavior.
1.6 Is There Evolution at Work?
Being continually adaptive, systems show continuous dynamic change.
This uses fewer or basic starting conditions and assumptions to grow into
complex system behavior. As time moves forward, certain conditions can be
changed to alter its behavior and future system states. Other components that
play a key role include geography or locations in the system. Geography can
influence in ways such as the following:
Communication span for each individual. Messages or communication
between individuals, which are limited to particular individuals in an
area. This gives them more information and act accordingly.
Messages influence personal behavior. Received messages can be used
to determine the next strategies to play based on the incoming information.
Influence of resource availability. Depending on their locations, each individual has various levels of resource available, that can affect its behavior. For example, in a ant colony model, if an ant comes across a stream
of water, it can locally change its on-course path, effectively adapting to
the situation and locality. Over time, the system will display a stronger