Near a bifurcation point a system experiences a critical slowdown. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node bifurcation where a metastable state disappears. The rate of activated escape W scales with the driving field amplitude A as ln W proportional, variant ( A(c) -A)(x...

Sergey Astakhov1 Oleg Astakhov2 Vladimir Astakhov3 Jürgen Kurths4 1Information Security of Automated Systems Dept., Yuri Gagarin Technical University of Saratov, Politekhnicheskaya st. 77, Saratov 410054, Russian Federation 2Department of Dynamic Modeling and Biomedical Engineering, Saratov State University, Astrakhanskaya st. 83, Saratov 410012, Russian Federation 3Radioelectronics and Telecom...

We argue that the Lukyanov-Shilnikov bifurcation of a saddle-node periodic orbit with noncentral homoclinics explains the effect of bi-stability observed in a neuron model based on a HodgkinHuxley formalism. In this model the dominating regime, depending on the initial state, can be either spiking oscillations or weakly irregular bursting ones. It is also shown how the bifurcation of the blue-s...

A few mathematical problems arising in the classical synchronization theory are discussed; especially those relating to complex dynamics. The roots of the theory originate in the pioneering experiments by van der Pol and van der Mark, followed by the theoretical studies by Cartwright and Littlewood. Today, we focus specifically on the problem on a periodically forced stable limit cycle emerging...

Coronary artery disease (CAD) is a multistaged process leading to a wide spectrum of pathoanatomic and clinical presentations.1 Given the diversity of underlying mechanisms, it is reasonable to involve distinct genetic modifiers along the cascade of events. Yet, molecular genetic association studies usually admix patients with stable and acute presentation, stenotic and ectatic forms of CAD, as...

What is the origin of rotational motion? An answer is presented through the study of the dynamics for spatially localized spots near codimension 2 singularity consisting of drift and peanut instabilities. The drift instability causes a head-tail asymmetry in spot shape, and the peanut one implies a deformation from circular to peanut shape. Rotational motion of spots can be produced by combinin...

We describe the dynamical and bifurcational behavior of two mutually inhibitory, leaky, neural units subject to external stimulus, random noise, and ‘priming biases.’ The model describes a simple forced choice experiment and accounts for varying levels of expectation and control. By projecting the model’s dynamics onto slow manifolds, using judicious linear approximations, and solving for one-d...