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Solitons, arising from nonlinear wave-matter interactions, stand out for their intrinsic stability during wave propagation and exceptional spectral characteristics. Their applications span diverse physical systems, including telecommunications, atomic clocks, and precise measurements. In recent years, significant strides have been made in developing cavity-optomechanics based approaches to generate optical frequency combs (FCs). In this study, we present an innovative approach, never explored before, that leverages elastomer membrane (EM)-cavity optomechanics to achieve the generation of soliton FCs, a highly sought-after phenomenon in the realm of nonlinear wave-matter interactions. Our method represents a significant breakthrough due to its streamlined simplicity, relying on a single continuous-wave (CW) laser pump and an externally applied acoustic wave exciting an EM-cavity, which gives rise to phonons, quantized vibrational energy states intrinsic to the elastomer's crystalline lattice structure. The mechanical resonator and electromagnetic cavity resonance are parametrically coupled within the microwave frequency range, collectively orchestrate the process of soliton FCs formation with remarkable efficiency. Numerical simulations and experimental observations demonstrate the emergence of multiple stable localized opto-mechanical wave packets, characterized by a narrow pulses time-domain response. Crucially, by setting the acoustic wave frequency to match the natural frequency of the EM resonator, the solitons' teeth are precisely spaced, and the EM's motion is significantly amplified, giving rise to a Kerr medium. The successful realization of optomechanical stable solitons represents a monumental advancement with transformative potential across various fields, including quantum computing and spectroscopy.

In this work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum driven by a coil-magnet interaction. The force between the magnetic elements and the resulting torque on the pendulum are derived using both the magnetic charges interaction model and the experimentally fitted interaction model. This enables the comparison between the two models. The current in the coil is taken first as a sinusoidal current and then as a square current. The comparison of the structure of each interaction model is conducted and it appears that they give qualitatively similar characteristics. The harmonic balance method is used to approximate the frequency responses of the pendulum leading to both symmetric and asymmetric or one-side (intrawell) oscillations. The two-parameters bifurcation diagrams are plotted showing the different dynamical behaviors considering the current amplitude and frequency as the control parameters. Good agreements are found between our theoretical results and experimental ones., Comment: Article published in the journal Mechanical Systems and Signal Processing. It consists of 18 pages

This paper presents a methodology of controlling the resonance energy exchange in mechanical system consisting of two weakly coupled magnetic pendulums interacting with the magnetic field generated by coils placed underneath. It is shown that properly guided magnetic fields can effectively change mechanical potentials in a way that the energy flow between the oscillators takes the desired direction. Studies were considered by using a specific set of descriptive functions characterizing the total excitation level, its distribution between the pendulums, and the phase shift. The developed control strategies are based on the observation that, in the case of antiphase oscillation, the energy is moving from the pendulum subjected to the repelling magnetic field, to the oscillator under the attracting field. In contrast, during the inphase oscillations, the energy flow is reversed. Therefore, closed-loop controller requires only the information about phase shift, which is easily estimated from dynamic state signals through the coherency index. Advantage of suggested control strategy is that the temporal rate of inputs is dictated by the speed of beating, which is relatively slow compared to the carrying oscillations.

In this paper, we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent, chimera, and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a different state where there is a coexistence of synchronized and asynchronized nodes of the network. One of the interesting results of the paper is the prevalence of double-well chimera states in both ring and ring-star network which has been first mentioned in the case of the memristive HR neuron model.

Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence of dangerous border collision bifurcation. In the case of one degree of freedom mechanical systems, it has already been shown that this phenomenon occurs under certain conditions. This paper proposes the same uncertainty of a two-degree freedom mechanical impacting system under specific requirements. This paper shows that the phenomena earlier reported in the case of one degree of freedom mechanical systems (like narrow band chaos, finger-shaped attractor, etc.) also occur in the two degrees of freedom mechanical impacting system. We have numerically predicted the narrowband chaos ensues under specific parameter settings. We have also shown that the narrowband chaos can be avoided under some parameter settings. At last, we demonstrate the numerical predictions experimentally by constructing an equivalent electronic circuit of the mechanical rig.

In this contribution, we have considered the collective behavior of the two as well as the network of heterogeneous coupled Hindmarsh Rose (HR) neurons. The heterogeneous models were made of a memristive 2D (HR) and the traditional 3D HR neurons. Investigating a model of two coupled neurons through an electrical synapse reveals dissipative properties. When control parameters are varied, the coupled neuron model exhibits rich dynamics, such as the periodic, quasi-periodic, and chaotic dynamics involving either bursting or spiking oscillations. For weak electrical coupling strength, non-synchronized motion is observed. But in the case of higher coupling strength, synchronized cluster states are observed. Besides, ring-star networks of up to 100 under three different heterogeneous topologies are being investigated, and various spatiotemporal patterns are explored. It is found that the spatiotemporal patterns depend on the topology of the heterogeneous network considered. A new clustered chimera state is revealed qualitatively via the recurrence plot. The cluster states are indicated in the ring and star configurations of the heterogeneous network. Single and double-well chimera states have been revealed in the ring and ring-star structures. Finally, an equivalent electronic circuit for the two coupled heterogeneous is designed and investigated in the PSIM simulation environment. A perfect match is observed between the results obtained from the designed analog circuit and the mathematical model of the two coupled neurons, which supports the fact that our obtained results are not related to an artifact.