Related papers: State transitions in the Morris-Lecar model under …
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
Many natural systems exhibit phase transition where external environmental conditions spark a shift to a new and sometimes quite different state. Therefore, detecting the behavior of a stochastic dynamic system such as the most probable…
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…
We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…
Systems driven by $\alpha$-stable noises could be very different from their Gaussian counterparts. Stationary states in single-well potentials can be multimodal. Moreover, a potential well needs to be steep enough in order to produce…
Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
Synchronization in various complex networks is significantly influenced by higher-order interactions combined with non-Gaussian stochastic perturbations, yet their mechanisms remain mainly unclear. In this paper, we systematically…
We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial…
In stochastic resonance, a periodically forced Brownian particle in a double-well potential jumps between minima at rare increments, the prediction of which poses a major theoretical challenge. Here, we use a path-integral method to find a…
The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probable paths is a key issue to understand the mechanism of…
We demonstrate that nonlocally coupled limit-cycle oscillators subject to spatiotemporally white Gaussian noise can exhibit a noise-induced transition to turbulent states. After illustrating noise-induced turbulent states with numerical…
Vortex based spin torque nano oscillators (STVOs) can present more complex dynamics than the spin torque induced gyrotropic (G) motion of the vortex core. The respective dynamic modes and the transition between them can be controlled by…
Many physical and biological systems exhibit intrinsic cyclic dynamics that are altered by random external perturbations. We examine continuous-time autonomous dynamical systems exhibiting a stable limit cycle, perturbed by additive…
The Kuramoto model (KM) of $n$ coupled phase-oscillators is analyzed in this work. The KM on a Cayley graph possesses a family of steady state solutions called twisted states. Topologically distinct twisted states are distinguished by the…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
Neuronal networks alternate between high- and low-activity regimes, known as up and down states. They also display rhythmic patterns essential for perception, memory consolidation, and sensory processing. Despite their importance, the…
We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from…
We investigate dynamics of recurrent neural networks with correlated noise to analyze the noise's effect. The mechanism of correlated firing has been analyzed in various models, but its functional roles have not been discussed in sufficient…
We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical…