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Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
Developing methods for detecting tipping phenomena at an early stage is an important problem in various fields such as ecology, medicine, and economics. A tipping phenomenon is characterized by a rapid transition resulting from the…
Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…
Rate-induced tipping occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states. We show that the addition of noise to the system can cause it to tip well below the critical rate at…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Many physical systems are forced by external inputs, which can sometimes take the form of chaotic variation. A particular example is found in applications related to weather and climate, where chaotic variation is prevalent across various…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
The glacial cycles are attributed to the climatic response of the orbital changes in the irradiance to the Earth. These changes in the forcing are to small to explain the observed climate variations as simple linear responses. Non-linear…
We propose predictive information, that is information between a long past of duration T and the entire infinitely long future of a time series, as a universal order parameter to study phase transitions in physical systems. It can be used,…
Time series forecasting is a fundamental tool with wide ranging applications, yet recent debates question whether complex nonlinear architectures truly outperform simple linear models. Prior claims of dominance of the linear model often…
It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…
The ability to reliably predict critical transitions in dynamical systems is a long-standing goal of diverse scientific communities. Previous work focused on early warning signals related to local bifurcations (critical slowing down) and…
Nucleation is considered near the pseudospinodal in a one-dimensional $\phi^4$ model with a non-conserved order parameter and long-range interactions. For a sufficiently large system or a system with slow relaxation to metastable…
A nonlinear model representing the tribological problem of a thin solid lubricant layer between two sliding periodic surfaces is used to analyze the phenomenon of hysteresis at pinning/depinning around a moving state rather than around a…