Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.  For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system.  The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926).  Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them.  Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined.  Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed.  Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey.  It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature.  And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

 The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

When multiplied out, the prey equation becomes

dx/dt = αx - βxy

 The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

F(t) = 1 - e ^ -λt 

Where  

• F(t) is the probability of failure  

• λ is the failure rate in 1/time unit (1/h, for example) 

• t is the observed service life (h, for example)

If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.  

The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period. 

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E' simile al D model (https://insightmaker.com/insight/206054/D-model-curve-di-Richards) ma qui la fase lag è esplicitamente inversamente proporzionale a mu. Questo semplifica alcuni calcoli quando mumax non è costante ma dipendente dalla temperatura. 

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E' un modello dinamico che assume che la fase lag sia dovuto all'accumulo di un composto essenziale (la cui quantità iniziale riflette lo stato iniziale delle cellule nell'ambiente E1, da cui provengono), secondo una cinetica di primo ordine, ad una velocità che dipende dall'ambiente E2. Il modello è lievemente modificato rispetto all'originale, per evitare che la quantità del prodotto essenziale tenda all'infinito. 

for more information, contact Dr. Ann Stapleton at: stapletona@uncw.edu

Description:

Adjust all sliders before beginning simulation. Make sure the A1A2 parameters are equal to the A2A1 parameters.