Related papers: Population Stability and Momentum
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
We introduce a novel type of random perturbation for the classical Lorenz flow in order to better model phenomena slowly varying in time such as anthropogenic forcing in climatology and prove stochastic stability for the unperturbed flow.…
Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors,…
Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among…
In order to control the growth of human population it is helpful to understand correctly the mechanism of growth, and the first essential step is to investigate current interpretations and reject any unscientific explanations. One of such…
Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been…
In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the notion of quantization of a probability measure. We connect this notion of stability to a geometric feature of the underlying…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
This paper investigates an energy conservation and dissipation -- passivity -- aspect of dynamic models in evolutionary game theory. We define a notion of passivity using the state-space representation of the models, and we devise…
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.
This study demonstrates how to construct the solutions of a more general form of population dynamics models via a blend of variational iterative method with Sumudu transform. In this paper, population growth models are formulated in the…
We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
Our research is concerned with studying behavioural changes within a dynamic system, i.e. health care, and their effects on the decision-making process. Evolutionary Game theory is applied to investigate the most probable strategy(ies)…
The origin of population-scale coordination has puzzled philosophers and scientists for centuries. Recently, game theory, evolutionary approaches and complex systems science have provided quantitative insights on the mechanisms of social…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
Nowadays, it is possible to record the activity of hundreds of cells at the same time in behaving animals. However, these data are often treated and analyzed as if they consisted of many independently recorded neurons. How can neuronal…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…