We consider a widely used form of models for ship maneuvering, whose nonlinearities entail continuous but nonsmooth second-order modulus terms. For such bifurcations straight motion are not amenable to standard center manifold reduction and normal forms. Based on recently developed analytical approach, we nevertheless determine the character local when stabilizing course with proportional contr...

We consider smooth systems limiting as ? ? 0 to piecewise-smooth (PWS) with a boundary-focus (BF) bifurcation. After deriving suitable local normal form, we study the dynamics for system sufficiently small but non-zero , using combination of geometric singular perturbation theory and blow-up . show that type BF bifurcation in PWS determines structure within an ?dependent domain which shrinks ze...

Bursting is one of the primary activity regimes of neurons. Our study is focused on determining a generic biophysical mechanism underlying the coexistence of the bursting and silent regimes observed in a neuron model. We show that the main ingredient for this mechanism is a saddle periodic orbit. The stable manifold of the orbit sets a threshold between the regimes of activity. Thus, the range ...

We study the dynamics of activity in the neural networks of enhanced integrate-and-fire elements (with random noise, refractory periods, signal propagation delay, decay of postsynaptic potential, etc.). We consider the networks composed of two interactive populations of excitatory and inhibitory neurons with all-to-all or random sparse connections. It is shown by computer simulations that the r...

We perform both analytical and numerical bifurcation analysis of an alternating forest grassland ecosystem model coupled with human interaction. The consists two nonlinear ordinary differential equations incorporating the perception value forest. system displays multiple steady states corresponding to different densities as well regimes characterized by stable unstable limit cycles. derive anal...

We study chains of strongly electrically coupled relaxation oscillators modeling dopamine neurons. When individual oscillators are in the regime close to an Andronov–Hopf bifurcation (AHB), the coupled system exhibits a variety of oscillatory behavior. We show that the proximity of individual oscillators to the AHB has a significant impact on the system dynamics in a wide range of parameters. I...

Based on Moore and Greitzer’s model [15], the surge behavior of axial flow compression system was found to be attributed to the appearance of Andronov-Hopf bifurcationin [12]. In this paper, we focus on the design of control law to prevent and/or delay the occurrence of the bifurcations, which will then suppress the surge behavior. Both types of linear dynamic state feedback and linear washout ...

We propose a route to spatiotemporal chaos for one-dimensional stationary patterns, which is a natural extension of the quasiperiodicity route for low-dimensional chaos to extended systems. This route is studied through a universal model of pattern formation. The model exhibits a scenario where stationary patterns become spatiotemporally chaotic through two successive bifurcations. First, the p...

A neural field model with multiple cell-to-cell feedback connections is investigated. Our model incorporates populations of ON and OFF cells, receiving sensory inputs with direct and inverted polarity, respectively. Oscillatory responses to spatially localized stimuli are found to occur via Andronov-Hopf bifurcations of stationary activity. We explore the impact of multiple delayed feedback com...

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...