Related papers: Hopf Bifurcation in a Generalized Goodwin Model wi…
The phenomenon of slow passage through a Hopf bifurcation is ubiquitous in multiple-timescale dynamical systems, where a slowly-varying quantity replacing a static parameter induces the solutions of the resulting slow-fast system to feel…
Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…
We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between "nearby" states. This is accomplished by defining a…
The population dynamics in a modified Leslie-Gower model with an additive Allee effect are highly sensitive to both parameters and initial population densities, leading to outcomes ranging from coextinction to sustained multistable steady…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
This paper pursues the study carried out by the authors in {\it Stability and Hopf bifurcation in the Watt governor system} \cite{smb}, focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system,…
An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by…
Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic…
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…
Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…
This paper empirically assesses predictions of Goodwin's model of cyclical growth regarding demand and distributive regimes when integrating the real and financial sectors. In addition, it evaluates how financial and employment shocks…
Planar switched system with dead-zone are analyzed. In particular, we consider the effects of perturbation of the linear control law from purely positional to position-velocity control. This type of perturbation leads to a novel Hopf-like…
Recently, research on the complex periodic behavior of multi-scale systems has become increasingly popular. Krupa et al. \cite{krupa2} provided a way to obtain relaxation oscillations in slow-fast systems through singular Hopf bifurcations…
We investigate the dynamics of a single breathing localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We show that variation of the delay time and the feedback strength can lead either…
We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second order…
Systems of ODEs coupled with the topology of a closed ring are common models in biology, robotics, electrical engineering, and many other areas of science. When the component systems and couplings are identical, the system has a cyclic…
For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…
We study the effect of migration between coupled populations, or patches, on the stability properties of multistrain disease dynamics. The epidemic model used in this work displays a Hopf bifurcation to oscillations in a single well mixed…
We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear…
Conceptual delay models have played a key role in the understanding of El Ni\~no-Southern Oscillation (ENSO) variability. Based on such delay models, we propose a novel scenario for the fabric of ENSO variability resulting from the subtle…