Simulation of certain oscillatory biological processes (original) (raw)
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Logical models provide insight about key control elements of biological networks. Based solely on the logical structure, we can determine state transition diagrams that give the allowed possible transitions in a coarse grained phase space. Attracting pathways and stable nodes in the state transition diagram correspond to robust attractors that would be found in several different types of dynamical systems that have the same logical structure. Attracting nodes in the state transition diagram correspond to stable steady states. Furthermore, the sequence of logical states appearing in biological networks with robust attracting pathways would be expected to appear also in Boolean networks, asynchronous switching networks, and differential equations having the same underlying structure. This provides a basis for investigating naturally occurring and synthetic systems, both to predict the dynamics if the structure is known, and to determine the structure if the transitions are known.
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We define a subclass of timed automata, called oscillator timed automata, suitable to model biological oscillators. The semantics of their interactions, parametric w.r.t. a model of synchronization, is introduced. We apply it to the Kuramoto model. Then, we introduce a logic, Kuramoto Synchronization Logic (KSL), and a model checking algorithm in order to verify collective synchronization properties of a population of coupled oscillators.
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El acceso a la versión del editor puede requerir la suscripción del recurso Access to the published version may require subscription This paper describes the use of grammatical evolution to obtain a predator-prey ecosystem of artificial beings associated with mathematical functions, whose fitness is also defined mathematically. The system supports the simultaneous evolution of several ecological niches and, through the use of standard measurements, makes it possible to explore the influence of the number of niches and the values of several parameters on "biological" diversity and similar functions. Sensitivity analysis tests have been made to find the effect of assigning different constant values to the genetic parameters that rule the evolution of the system and the predator-prey interaction, or of replacing them by functions of time. One of the parameters (predator efficiency) was found to have a critical range, outside which the ecologies are unstable; two others (genetic shortening rate and predator-prey fitness comparison logistic amplitude) are critical just at one side of the range), the others are not critical. The system seems quite robust, even when one or more parameters are made variable during a single experiment, without leaving their critical ranges. Our results also suggest that some of the features of biological evolution depend more on the genetic substrate and natural selection than on the actual phenotypic expression of that substrate.
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A mathematical model is presented that describes the time course of maturation of a population of organisms. The model assumes that individuals are subject to intermittent pauses in development. When applied to the transition from one observable phase of development to another this model predicts a dormant period followed by the abrupt onset of maturation which is skewed over time. Applications of this model are discussed for biological systems developing in constant or fluctuating environmental conditions.
A Mathematical Model of Evolutionary Systems
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