Organizing competitor analysis systems

Limit cycles for competitor–competitor–mutualist Lotka–Volterra systems

It is known that a limit cycle (or periodic coexistence) can occur in a competitor–competitor–mutualist Lotka–Volterra system  ẋ1 = x1(r1 − a11x1 − a12x2 + a13x3), ẋ2 = x2(r2 − a21x1 − a22x2 + a23x3), ẋ3 = x3(r3 + a31x1 + a32x2 − a33x3), where ri , ai j are positive real constants [X. Liang, J. Jiang, The dynamical behavior of type-K competitive Kolmogorov systems and its applications to 3-di...

Foundations for Organizing Systems

Steps toward numerical mode analysis of organizing systems.

A well established method to analyze dynamical systems described by coupled nonlinear differential equations is to determine their normal modes and reduce the dynamics, by adiabatic elimination of stable modes, to a much smaller system for the amplitudes of unstable modes and their nonlinear interactions. So far, this analysis is possible only for idealized symmetric model systems. We aim to bu...

Analysis of Complex Systems using the Self Organizing Map

The Self Organizing Map SOM is a powerful neural network method for the analysis and visualization of high dimensional data It maps nonlinear statistical relationships between high dimensional input data into simple geometric relationships on a usually two dimensional grid The mapping roughly preserves the most important topological and metric relationships of the original data elements and thu...

Self-Organizing Systems

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