​Predator-prey models are the building masses of the bio-and environments as bio masses are become out of their asset masses. Species contend, advance and scatter essentially to look for assets to support their battle for their very presence. Contingent upon their particular settings of uses, they can take the types of asset resource-consumer, plant-herbivore, parasite-have, tumor cells- immune structure, vulnerable irresistible collaborations, and so on. They manage the general misfortune win connections and thus may have applications outside of biological systems. At the point when focused connections are painstakingly inspected, they are regularly in actuality a few types of predator-prey communication in simulation. 

 

Looking at Lotka-Volterra Model:

The well known Italian mathematician Vito Volterra proposed a differential condition model to clarify the watched increment in predator fish in the Adriatic Sea during World War I. Simultaneously in the United States, the conditions contemplated by Volterra were determined freely by Alfred Lotka (1925) to portray a theoretical synthetic response wherein the concoction fixations waver. The Lotka-Volterra model is the least complex model of predator-prey communications. It depends on direct per capita development rates, which are composed as f=b−py and g=rx−d. 

A detailed explanation of the parameters:

• The parameter b is the development rate of species x (the prey) without communication with species y (the predators). Prey numbers are reduced by these collaborations: The per capita development rate diminishes (here directly) with expanding y, conceivably getting to be negative. 

• The parameter p estimates the effect of predation on x˙/x. 

• The parameter d is the death rate of species y without connection with species x. 

• The term rx means the net rate of development of the predator population in light of the size of the prey population.

Reference:

http://www.scholarpedia.org/article/Predator-prey_model

 

Education Chaos Ecology Biology Population

​death ratehttps://www.cdc.gov/nchs/fastats/deaths.htm

birth ratehttps://www.cdc.gov/nchs/fastats/births.htm

population, and total immigration ratehttps://www.cia.gov/library/publications/the-world-factbook/geos/us.html

Biology

Biology

Biology

Biology

Simulation of MTBF with controls

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)
The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early LifeIf 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.
Useful Life
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.  
Wearout
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. 

Environment Economics Finance Mathematics Physics Biology Health Fractals Chaos TURBULENCE Engineering Navier Stokes Science Demographics Population Growth BIFURCATIONS MTBF Risk Failure Strategy

Biology

a food web for my project

Biology

Biology

Biology Biodiesel Algae

Biology

Biology

Biology FOOD WEB Food Chain

Examples of flows

Environment Biology Growth

Biology Carbon Cycle Biogeochemical

Level of biological organization linking cell level division and population level evolution

Health Care Biology Multiscale

A model of the exponential growth and collapse of E. coli.

Exponential Growth Collapse Bacteria Biology Microbiology Science

Simulation of MTBF with controls

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)
The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early LifeIf 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.
Useful Life
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.  
Wearout
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. 

Environment Economics Finance Mathematics Physics Biology Health Fractals Chaos TURBULENCE Engineering Navier Stokes Science Demographics Population Growth BIFURCATIONS MTBF Risk Failure Strategy

Pennsylvania plants and animals

Biology Ecology

Biology

Biology

OVERSHOOT GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite limited size working capacity containers (villages communities)

Environment Economics Finance Mathematics Physics Biology Health Fractals Chaos TURBULENCE Engineering Navier Stokes Science Demographics Population Growth Strategy Weather

STRESSFUL!!!!!!!!!!!!!

Biology

Физический смысл уравненийМодель Лотки-Вольтерры делает ряд предположений об окружающей среде и эволюции популяций хищников и жертв:
1. Хищная популяция всегда находит достаточно пищи.2. Продовольственная обеспеченность популяции хищника полностью зависит от размера популяции жертвы.3. Скорость изменения численности населения пропорциональна его численности.4. В ходе этого процесса окружающая среда не меняется в пользу одного вида, и генетическая адаптация не имеет существенного значения.5. Хищники обладают безграничным аппетитом.Поскольку используются дифференциальные уравнения, решение является детерминированным и непрерывным. Это, в свою очередь, означает, что поколения как хищника, так и жертвы постоянно пересекаются.
ДобычаКогда умножается, уравнение добычи становится
dx/dt = αx - βxy  Предполагается, что добыча имеет неограниченный запас пищи и размножается экспоненциально, если только она не подвержена хищничеству; этот экспоненциальный рост представлен в приведенном выше уравнении термином  αx. Предполагается, что скорость хищничества на добыче пропорциональна скорости, с которой встречаются хищники и добыча; это представлено выше в виде βxy.Если либо x, либо y равно нулю, то хищничества быть не может.С помощью этих двух терминов приведенное выше уравнение можно интерпретировать следующим образом: изменение численности добычи определяется ее собственным ростом минус скорость, с которой она охотится.ХищникиУравнение хищника становится

dy/dt =  - 

В этом уравнении,  представляет рост популяции хищника. (Обратите внимание на сходство со скоростью хищничества; однако используется другая константа, поскольку скорость роста популяции хищника не обязательно равна скорости, с которой он потребляет добычу).  представляет собой уровень потерь хищников вследствие естественной смерти или эмиграции; это приводит к экспоненциальному распаду в отсутствие добычи.

Следовательно, уравнение выражает изменение популяции хищников как рост, подпитываемый запасом пищи, минус естественная смерть.

Education Chaos Ecology Biology Population