Are they good to eat? Does the person who creates the systems think about the complexity of the recipe?
Let's define a system:
A system is a set formed by multiple interacting elements in such a way as to constitute a single entity and organized to achieve a predetermined goal. A system is a set of parts or elements related in such a way as to constitute a whole, which has meaning in a certain context. A system is a set of parts related in such a way as to form a whole and/or function in a certain way.
Invariant system vs variant system
Invariant systems: a system is defined as invariant or stationary if it responds equally to the same stimuli, at different times. (Examples: a calculator, a can dispenser).
Variant system: a system is defined as variant or deteriorable when the same inputs correspond to different outputs. (Examples: a missile traveling from Earth to the Moon consuming solid fuel).
Deterministic system: a system is defined as deterministic when the transition and transformation functions are defined in such a way as to allow the determination of the state value and outputs in a unique way. (Examples: irrigation systems, every time the switch is pressed, a sprayer turns on; or a production line).
Stochastic system: a system is defined as stochastic when one of the two functions is regulated by a probabilistic nature. (Examples: amount of light during the day, atmospheric turbulence, number of patients in a hospital).
Examples:
1.Invariant deterministic= The laws of physics are invariant (as far as is currently known).
2.Variant deterministic= Often, variant systems derive from inputs to the system (coming from external systems) and intentionally not included in the model.
3.Variant stochastic= From a practical point of view, a stochastic process is a form of representation of a quantity that varies over time in a random way (for example, an electrical signal containing information or modulated, the number of cars passing over a bridge, etc.) and with certain characteristics.
4. Invariant stochastic= In a chemical reaction, the transition probabilities from state i to state j in a step do not depend on the instant being considered or when such a transition occurs.
INVARIANT SYSTEM: a system from which, given certain inputs, I always receive the same outputs (coffee machine (the output is not influenced by variables))
VARIANT SYSTEM: a system in which there are non-negligible variables that determine the output (the output in these systems will depend on the changing parameters)
(weather forecasts (the output is influenced by variables))
DETERMINISTIC SYSTEM: if, subjected to the same initial conditions and the same stimuli, it behaves evolving always in the same way (remote control)
STOCHASTIC SYSTEM: if, subjected to the same initial conditions and the same stimuli, it behaves evolving in a random or unpredictable way. Roulette (the output is random, it does not depend on the input which in this case is the bet)
Deterministic system: A system is defined as deterministic if, subjected to the same initial conditions and the same stimuli, it behaves evolving always in the same way. The system is describable by a mathematical function. EXAMPLES: calculator, computer…
Sochastic system: A system is defined as stochastic if, subjected to the same initial conditions and the same stimuli, it behaves evolving in a random or unpredictable way. EXAMPLES: double pendulum, fluid turbulence, brownian motion…
VARIANT DETERMINISTIC: movement of a projectile, trajectory of an arrow…
INVARIANT DETERMINISTIC: calculator, drawing program functions…
VARIANT STOCHASTIC: movement of a turbulent fluid, chaotic double pendulum, position of the electron around the nucleus…
INVARIANT STOCHASTIC: slot machine, dice roll…
