SIAM Journal on Applied Dynamical Systems http://scitation.aip.org/ SIAM Journal on Applied Dynamical Systems Selection of Ground States in the Zero Temperature Limit for a One-Parameter Family of Potentials http://link.aip.org/link/?SJA/11/243/1&agg=rss A. T. Baraviera, R. Leplaideur, and A. O. Lopes<br/> For the subshift of finite type $\Sigma=\{0,1,2\}^{\mathbb{N}}$ we study the convergence and the selection at temperature zero of the Gibbs measure associated to a nonlocally constant Holder potential which admits exactly two maximizing ergodic measures. These measures are Dirac measures at two dif ... [SIAM J. Appl. Dyn. Syst. 11, 243 (2012)] published Thu Feb 2, 2012. A Fast-Slow Analysis of the Dynamics of REM Sleep http://link.aip.org/link/?SJA/11/212/1&agg=rss Cecilia G. Diniz Behn and Victoria Booth<br/> Waking and sleep states are regulated by the coordinated activity of a number of neuronal populations in the brainstem and hypothalamus whose synaptic interactions compose a sleep-wake regulatory network. Physiologically based mathematical models of the sleep-wake regulatory network contain mechani ... [SIAM J. Appl. Dyn. Syst. 11, 212 (2012)] published Tue Jan 31, 2012. Canonical Discontinuous Planar Piecewise Linear Systems http://link.aip.org/link/?SJA/11/181/1&agg=rss Emilio Freire, Enrique Ponce, and Francisco Torres<br/> The family of Filippov systems constituted by planar discontinuous piecewise linear systems with two half-plane linearity zones is considered. Under generic conditions that amount to the boundedness of the sliding set, some changes of variables and parameters are used to obtain a Lienard-like canon ... [SIAM J. Appl. Dyn. Syst. 11, 181 (2012)] published Tue Jan 31, 2012. Canard-Like Explosion of Limit Cycles in Two-Dimensional Piecewise-Linear Models of FitzHughNagumo Type http://link.aip.org/link/?SJA/11/135/1&agg=rss Horacio G. Rotstein, Stephen Coombes, and Ana Maria Gheorghe<br/> We investigate the mechanism of abrupt transition between small- and large amplitude oscillations in fast-slow piecewise-linear (PWL) models of FitzHughNagumo (FHN) type. In the context of neuroscience, these oscillatory regimes correspond to subthreshold oscillations and action potentials (spikes) ... [SIAM J. Appl. Dyn. Syst. 11, 135 (2012)] published Thu Jan 26, 2012. Switching in Mass Action Networks Based on Linear Inequalities http://link.aip.org/link/?SJA/11/110/1&agg=rss Carsten Conradi and Dietrich Flockerzi<br/> Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space (associated with different biochemical functions). Switching is oft ... [SIAM J. Appl. Dyn. Syst. 11, 110 (2012)] published Thu Jan 26, 2012. Efficient Automation of Index Pairs in Computational Conley Index Theory http://link.aip.org/link/?SJA/11/82/1&agg=rss Rafael Frongillo and Rodrigo Trevino<br/> We present new methods of automating the construction of index pairs, essential ingredients of discrete Conley index theory. These new algorithms are further steps in the direction of automating computer-assisted proofs of semiconjugacies from a map on a manifold to a subshift of finite type. We ap ... [SIAM J. Appl. Dyn. Syst. 11, 82 (2012)] published Tue Jan 24, 2012. Noise-Induced Behaviors in Neural Mean Field Dynamics http://link.aip.org/link/?SJA/11/49/1&agg=rss Jonathan Touboul, Geoffroy Hermann, and Olivier Faugeras<br/> The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons with linear intrinsic dynamics and nonlinear coupling, belo ... [SIAM J. Appl. Dyn. Syst. 11, 49 (2012)] published Fri Jan 13, 2012. An Algebraic Approach to Reverse Engineering Finite Dynamical Systems Arising from Biology http://link.aip.org/link/?SJA/11/31/1&agg=rss Alan Veliz-Cuba<br/> Finite dynamical systems have been used successfully in modeling biological processes. When certain regulatory mechanisms of a biological system or a model are unknown it is important to be able to identify the best model with the available data. In this context, reverse engineering of finite dynam ... [SIAM J. Appl. Dyn. Syst. 11, 31 (2012)] published Tue Jan 10, 2012. Breathers and Q-Breathers: Two Sides of the Same Coin http://link.aip.org/link/?SJA/11/1/1&agg=rss T. Penati and S. Paleari<br/> We construct, and approximate from the continuum, two-parameter families of time periodic, small amplitude, localized solutions, for both the focusing and defocusing finite discrete nonlinear Schrodinger models, with Dirichlet boundary conditions. Within such families, depending on the parameters, ... [SIAM J. Appl. Dyn. Syst. 11, 1 (2012)] published Tue Jan 10, 2012. Two Degenerate Boundary Equilibrium Bifurcations in Planar Filippov Systems http://link.aip.org/link/?SJA/10/1525/1&agg=rss Fabio Dercole, Fabio Della Rossa, Alessandro Colombo, and Yuri A. Kuznetsov<br/> We contribute to the analysis of codimension-two bifurcations in discontinuous systems by studying all equilibrium bifurcations of 2D Filippov systems that involve a sliding limit cycle. There are only two such local bifurcations: (1) a degenerate boundary focus, which we call the homoclinic bounda ... [SIAM J. Appl. Dyn. Syst. 10, 1525 (2011)] published Tue Dec 13, 2011.