Global ETD Search
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Showing 1 to 14 of 14 for “"discrete dynamical systems"”.
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Omega-Limit Sets of Discrete Dynamical Systems
… and important objects in the study of discrete dynamical systems. Using a variety of methods, we present and extend existing results in this area of research. Of particular interest is the property of internal chain transitivity, and we present several characterizations of omega-limit …
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Discrete dynamical systems in solving H-equations
Three discrete dynamical models are used to solve the Chandrasekhar H-equation with a positive or negative characteristic function. Two of them produce series of continuous functions which converge to the solution of the H-equation. An iteration model of the nth approximation for the H-equation is …
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NODE INFLUENCE IN NETWORK-BASED DISCRETE DYNAMICAL SYSTEMS
Many complex systems can be modeled as network-based discrete dynamical systems, where individual nodes (representing some variable of interest) are connected by edges that describe their interactions. Each node can take on different states relevant to the network under investigation (for example, …
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Modeling and Analysis of the Collective Dynamics of Large-Scale Multi-Agent Systems
Keywords. multi-agent systems, distributed artificial intelligence, theoretical computer science, formal methods, computational complexity, cellular and network automata, agent-based modeling, discrete dynamical systems, complex systems.
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A stochastic treatment of reaction and diffusion
… analysis consists of Boltzmann maps, which are discrete time dynamical systems that describe the time evolution of the normalized concentrations of the chemicals in the reactions. Moreover, the use of these maps allows us to draw conclusions about the continuous dynamical systems that the law of …
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A Mathematical Model of a Denitrification Metabolic Network in Pseudomonas aeruginosa
… testable hypotheses generation using polynomial dynamical systems and stochastic discrete dynamical systems. Analysis of the long-term behavior of the system changing the concentration level of oxygen, nitrate, and phosphate suggests that phosphate highly affects the denitrification performance …
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Nonsmooth Bifurcations and the Role of Density Dependence in a Chaotic Infectious Disease Model
Discrete dynamical systems can exhibit rich and interesting dynamics at lower dimensions (and co-dimensions) than that of ODE models. Classically, the minimal dimension to observe chaotic behavior in an ODE model is three; whereas it can be achieved in a one-dimensional discrete map. It is often …
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Generalizations of Threshold Graph Dynamical Systems
… their social, political, and economic impacts. Discrete dynamical systems (discrete in time and discrete in agent states) are often used to quantify contagion propagation in populations that are cast as graphs, where vertices represent agents and edges represent agent interactions. We refer to …
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Centre Manifold Theory for some continuous and Discrete Epidemiological models
… of the backward bifurcation phenomenon for dynamical systems, with emphasis on a “simple” SIS model with vaccination and a “complex” malaria model. We re-centre the reduction theorem in C. Castillo-Chavez and B. Song (2004) and highlight its advantage over the legendary power series …
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Qualitative modeling of chaotic logical circuits and walking droplets: a dynamical systems approach
… thinking differently about these well-studied systems. Specifically, there has been great interest in chaotic logical circuits and hydrodynamic quantum analogs. Traditional logical circuits are designed with minimal uncertainty. While this is straightforward to achieve with electronic logic, …
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Algebraic theory for discrete models in systems biology
This dissertation develops algebraic theory for discrete models in systems biology. Many discrete model types can be translated into the framework of polynomial dynamical systems (PDS), that is, time- and state-discrete dynamical systems over a finite field where the transition function for each …
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Robustness Analysis of Gene Regulatory Networks
… GRNs are represented in the time- and statediscrete framework of Stochastic Discrete Dynamical Systems (SDDS), which captures the cell-inherent stochasticity. Each gene has finitely many different concentration levels and its concentration at the next time step is determined by a …
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Iterates of functions defined in terms of digital representations of the integers
For a fixed base, John H. Conway’s RATS sequences are generated by iterating the following procedure on an initial integer: Reverse the digits of the integer, Add the reversal to the original, Then Sort the resulting digits in increasing order. For example, 334+433=767, which gets sorted into 677. …