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This work provides a geometric approach to the study of bifurcation and rate induced transitions in a class of non-autonomous systems referred to herein as $\textit{asymptotically slow-fast systems}$, which may be viewed as 'intermediate'…
Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
We present a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In…
The chaotic properties of Newton-Leipnik system are discussed from the view point of strange attractors. Previously, two strange attractors of this system were illustrated which occured from two different initial conditions under the same…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
We propose a novel and fully data driven control scheme which relies on machine learning (ML). Exploiting recently developed ML-based prediction capabilities of complex systems, we demonstrate that nonlinear systems can be forced to stay in…
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of…
This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
Critical transitions or regime shifts are sudden and unexpected changes in the state of an ecosystem, that are usually associated with dangerous levels of environmental change. However, recent studies show that critical transitions can also…
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…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
We introduce system norms which assess transient behavior of stable Linear Time-Invariant (LTI) systems. This allows us to address undesired responses to initial conditions, finite resource consumption signals, or persistent perturbations.…