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This paper presents a general theory that aims at explaining timescales observed empirically in technology transitions and predicting those of future transitions. This framework is used further to derive a theory for exploring the dynamics…
The notion of the "adjacent possible" has been advanced to theorize the generation of novelty across many different research domains. This study is an attempt to examine in what way the notion can be made empirically useful for innovation…
Product cannibalisation is a well-known phenomenon in marketing and technological research and describes the case when a new product steals sales from another product under the same brand. A very special case of cannibalisation may occur…
At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if…
Almost by definition, radical innovations create a need to revise existing classification systems. In this paper, we argue that classification system changes and patent reclassification are common and reveal interesting information about…
To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…
The possibility to use competitive evolutionary algorithms to generate long-term progress is normally prevented by the convergence on limit cycle dynamics in which the evolving agents keep progressing against their current competitors by…
Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
The decomposable branching processes are relatively less studied objects, particularly in the continuous time framework. In this paper, we consider various variants of decomposable continuous time branching processes. As usual practice in…
Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space…
We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…
This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a…
The Lotka-Euler equation is a mathematical expression used to study population dynamics and growth, particularly in the context of demography and ecology. The growth rate $\lambda$ is the speed at which an individual produce their…
We study several models of growth driven by innovation and imitation by a continuum of firms, focusing on the interaction between the two. We first investigate a model on a technology ladder where innovation and imitation combine to…
The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the…
There are clear benefits associated with a particular consumer choice for many current markets. For example, as we consider here, some products might carry environmental or `green' benefits. Some consumers might value these benefits while…
Innovation is to organizations what evolution is to organisms: it is how organisations adapt to changes in the environment and improve. Governments, institutions and firms that innovate are more likely to prosper and stand the test of time;…
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…