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Kolmogorov Population Model
In biomathematics, the Kolmogorov population model, also known as the Kolmogorov equations in population dynamics, is a mathematical model, mathematical framework developed by Soviet mathematician Andrei Kolmogorov in 1936 that generalizes predator-prey interactions and population dynamics. The model was an improvement over earlier predator-prey models, notably the Lotka–Volterra equations, by incorporating more realistic biological assumptions and providing a Qualitative theory of differential equations, qualitative analysis of population dynamics. History The development of the Kolmogorov population model was influenced by Kolmogorov's early interest in biology during his schoolboy years. Despite being primarily known for his contributions to probability theory and information theory, Kolmogorov made several large contributions to biomathematics. The model was particularly inspired by the work of Italian people, Italian physicist Vito Volterra, who had developed his predator- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrej Nikolajewitsch Kolmogorov
Andrej is the form of the given name Andrew used in Slovak language, Slovak, Croatian language, Croatian and Slovene language, Slovene. Notable individuals with the given name Andrej *Andrej Babiš (born 1954), Czech politician *Andrej Bajuk (1943–2011), Slovene politician and economist *Andrej Čadež (born 1942), Slovene physicist and astrophysicist *Andrej Karpathy (born 1986), Slovak-Canadian computer scientist *Andrej Kiska (born 1963), Slovak politician and businessman *Andrej Kramarić (born 1991), Croatian football player *Andrej Meszároš (born 1985), Slovak ice hockey player *Andrej Plenković (born 1970), Croatian politician *Andrej Pohar (born 1974), Slovenian badminton player *Andrej Sekera (born 1986), Slovak hockey player *Andrej Stančík (born 1995), Slovak politician *Andrej Stojaković (born 2004), Serbian–Greek basketball player {{given name, nocat Slovak masculine given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War I
World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting took place mainly in European theatre of World War I, Europe and the Middle Eastern theatre of World War I, Middle East, as well as in parts of African theatre of World War I, Africa and the Asian and Pacific theatre of World War I, Asia-Pacific, and in Europe was characterised by trench warfare; the widespread use of Artillery of World War I, artillery, machine guns, and Chemical weapons in World War I, chemical weapons (gas); and the introductions of Tanks in World War I, tanks and Aviation in World War I, aircraft. World War I was one of the List of wars by death toll, deadliest conflicts in history, resulting in an estimated World War I casualties, 10 million military dead and more than 20 million wounded, plus some 10 million civilian de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predator-prey Interactions
Predation is a biological interaction in which one organism, the predator, kills and eats another organism, its prey. It is one of a family of common feeding behaviours that includes parasitism and micropredation (which usually do not kill the host) and parasitoidism (which always does, eventually). It is distinct from scavenging on dead prey, though many predators also scavenge; it overlaps with herbivory, as seed predators and destructive frugivores are predators. Predation behavior varies significantly depending on the organism. Many predators, especially carnivores, have evolved distinct hunting strategies. Pursuit predation involves the active search for and pursuit of prey, whilst ambush predators instead wait for prey to present an opportunity for capture, and often use stealth or aggressive mimicry. Other predators are opportunistic or omnivorous and only practice predation occasionally. Most obligate carnivores are specialized for hunting. They may have acute s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Biology
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to test scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms interchange; overlapping as Artificial Immune Systems of Amorphous Computation. Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strange Attractors
In the mathematics, mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. In finite-dimensional systems, the evolving variable may be represented algebraically as an ''n''-dimensional Coordinate vector, vector. The attractor is a region in space (mathematics), ''n''-dimensional space. In Physics, physical systems, the ''n'' dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in Economics, economic systems, they may be separate variables such as the inflation rate and the unemployment rate. If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented Geometry, geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Stability
In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy. During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation: *the state of least energy is the only one the system will inhabit for an indefinite length of time, until more external energy is added to the system (unique "absolut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillations
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert H
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of ''Hrōþ, Hruod'' () "fame, glory, honour, praise, renown, godlike" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin.Reaney & Wilson, 1997. ''Dictionary of English Surnames''. Oxford University Press. It is also in use Robert (surname), as a surname. Another commonly used form of the name is Rupert (name), Rupert. After becoming widely used in Continental Europe, the name entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta (given name), Roberta. The Italian, Portuguese, and Spanish form is Roberto (given name), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Rosenzweig
Michael L. Rosenzweig (born 1941) is a professor of ecology and evolutionary biology at the University of Arizona. He developed and popularized the concept of reconciliation ecology. He received his Ph.D. in zoology at the University of Pennsylvania in 1966 and has held a number of academic positions around the United States. Rosenzweig has a large body of editorial work spanning from 1977 to present, founding the journals ''Evolutionary Ecology'' and ''Evolutionary Ecology Research'' as well as the publishing house, Evolutionary Ecology Ltd. with the help of his wife Carole. When the ''Journal of Evolutionary Ecology'' was sold and the prices were to be raised, he stepped down from his editor in chief position and founded Evolutionary Ecology Ltd, which published the journal ''Evolutionary Ecology Research''. Rosenzweig's articles cover topics ranging from species diversity to predation dynamics and includes work on environmental issues and public policy. He has published three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecologist
Ecology () is the natural science of the relationships among living organisms and their environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere levels. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and is the study of abundance, biomass, and distribution of organisms in the context of the environment. It encompasses life processes, interactions, and adaptations; movement of materials and energy through living communities; successional development of ecosystems; cooperation, competition, and predation within and between species; and patterns of biodiversity and its effect on ecosystem processes. Ecology has practical applications in fields such as conservation biology, wetland management, natural resource management, and human ecology. The word ''ecology'' () was coined in 1866 by the German scientist Ern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volterra Equations
Volterra (; Latin: ''Volaterrae'') is a walled mountaintop town in the Tuscany region of Italy. Its history dates from before the 8th century BC and it has substantial structures from the Etruscan, Roman, and Medieval periods. History Volterra, known to the ancient Etruscans as ''Velathri'' or ''Vlathri'' and to the Romans as ''Volaterrae'', is a town and ''comune'' in the Tuscany region of Italy. The site is believed to have been continuously inhabited as a city since at least the end of the 8th century BC. The town was a Bronze Age settlement of the Proto-Villanovan culture. It became an important Etruscan centre as one of the "twelve cities" of the Etruscan League. It was allied to Rome at the end of the 3rd century BC and became a municipium. The wealthy Caecina family lived here and Gaius Caecina Largus and the eminent Aulus Caecina Severus (consul 2–1 BC) built the theatre and probably other monuments. Other important families here were the Persii and the Lael ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carrying Capacity
The carrying capacity of an ecosystem is the maximum population size of a biological species that can be sustained by that specific environment, given the food, habitat, water, and other resources available. The carrying capacity is defined as the environment's maximal load, which in population ecology corresponds to the population equilibrium, when the number of deaths in a population equals the number of births (as well as immigration and emigration). Carrying capacity of the environment implies that the resources extraction is not above the rate of regeneration of the resources and the wastes generated are within the assimilating capacity of the environment. The effect of carrying capacity on population dynamics is modelled with a logistic function. Carrying capacity is applied to the maximum population an environment can support in ecology, agriculture and fisheries. The term carrying capacity had been applied to a few different processes in the past before finally being appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
