12,047 research outputs found
Qualitative analysis of the dynamics of the time delayed Chua's circuit
IEEE TRANS. CIRCUITS SYST.
Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models
We use the Litvinov-Maslov correspondence principle to reduce and hybridize
networks of biochemical reactions. We apply this method to a cell cycle
oscillator model. The reduced and hybridized model can be used as a hybrid
model for the cell cycle. We also propose a practical recipe for detecting
quasi-equilibrium QE reactions and quasi-steady state QSS species in
biochemical models with rational rate functions and use this recipe for model
reduction. Interestingly, the QE/QSS invariant manifold of the smooth model and
the reduced dynamics along this manifold can be put into correspondence to the
tropical variety of the hybridization and to sliding modes along this variety,
respectivelyComment: conference SASB 2011, to be published in Electronic Notes in
Theoretical Computer Scienc
Effects of Transport Memory and Nonlinear Damping in a Generalized Fisher's Equation
Memory effects in transport require, for their incorporation into reaction
diffusion investigations, a generalization of traditional equations. The
well-known Fisher's equation, which combines diffusion with a logistic
nonlinearity, is generalized to include memory effects and traveling wave
solutions of the equation are found. Comparison is made with alternate
generalization procedures.Comment: 6 pages, 4 figures, RevTeX
Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos
A novel view for the emergence of chaos in Lorenz-like systems is presented.
For such purpose, the Lorenz problem is reformulated in a classical mechanical
form and it turns out to be equivalent to the problem of a damped and forced
one dimensional motion of a particle in a two-well potential, with a forcing
term depending on the ``memory'' of the particle past motion. The dynamics of
the original Lorenz system in the new particle phase space can then be
rewritten in terms of an one-dimensional first-exit-time problem. The emergence
of chaos turns out to be due to the discontinuous solutions of the
transcendental equation ruling the time for the particle to cross the
intermediate potential wall. The whole problem is tackled analytically deriving
a piecewise linearized Lorenz-like system which preserves all the essential
properties of the original model.Comment: 48 pages, 25 figure
Reduction of dynamical biochemical reaction networks in computational biology
Biochemical networks are used in computational biology, to model the static
and dynamical details of systems involved in cell signaling, metabolism, and
regulation of gene expression. Parametric and structural uncertainty, as well
as combinatorial explosion are strong obstacles against analyzing the dynamics
of large models of this type. Multi-scaleness is another property of these
networks, that can be used to get past some of these obstacles. Networks with
many well separated time scales, can be reduced to simpler networks, in a way
that depends only on the orders of magnitude and not on the exact values of the
kinetic parameters. The main idea used for such robust simplifications of
networks is the concept of dominance among model elements, allowing
hierarchical organization of these elements according to their effects on the
network dynamics. This concept finds a natural formulation in tropical
geometry. We revisit, in the light of these new ideas, the main approaches to
model reduction of reaction networks, such as quasi-steady state and
quasi-equilibrium approximations, and provide practical recipes for model
reduction of linear and nonlinear networks. We also discuss the application of
model reduction to backward pruning machine learning techniques
- âŠ