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We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
Ising Machines (IMs) are physical systems designed to find solutions to combinatorial optimization (CO) problems mapped onto the IM via the coupling strengths of its binary spins. Using the intrinsic dynamics and different annealing…
Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details.…
Power-based output feedback compensator for oscillatory systems is proposed. The average input-output power of an oscillatory signal serves as an equivalent control effort, while the unknown amplitude and frequency of oscillations are…
We investigate the classical-quantum correspondence in the inverted harmonic oscillator (IHO) system. It is shown that the out-of-time-order correlators (OTOCs) which the initial states are located at any position in the IHO system possess…
Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from…
The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast…
In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the…
Feedback loops are major components of biochemical systems. Many systems show multiple such (positive or negative) feedback loops. Nevertheless, very few quantitative analyses address the question how such multiple feedback loops evolved.…
Electronic structure calculations were carried out on the compound GdBaCo$_2$O$_{5.5}$. The electronic structure variation with a change in the spin state of the Co$^{3+}$ ion in an octahedral environment has been studied. All the…
A driven linear oscillator and a feedback mechanism are two necessary elements of any classical periodic clock. Here, we introduce a novel, fully quantum clock using a driven oscillator in the quantum regime and coherent quantum feedback.…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We…
In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…
This paper applies a recent result determining periodic orbits on the basis of first integrals, for Li\'enard systems. By solving a first order ODE with singularities, a crucial result is proved to locate intervals of single and isolated…
In a previous paper the \textit{real} evolution of the system of ODEs \ddot{z}_{n} + z_{n}=\sum\limits_{m = 1, m \ne n}^{N} g_{nm}{(z_{n} - z_{m})} ^{- 3}, z_{n} \equiv z_{n}(t), \qquad \dot {z}_{n} \equiv \frac{d z_{n}(t)}{dt}, \qquad n =…
In this paper the existence and unicity of a stable periodic orbit is proven, for a class of piecewise affine differential equations in dimension 3 or more, provided their interaction structure is a negative feedback loop. It is also shown…
The problem of maintaining the output of a positive time-invariant single-input single-output system within a predefined corridor of values is treated. For third-order plants possessing a certain structure, it is proven that the problem is…