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pp. 105-108 | DOI: 10.5890/JVTSD.2025.06.001
Jose M. Balthazar, Paulo B. Goncalves, Angelo M. Tusset, Gregory Litak
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This special issue contains 7 papers selected, after review, from the papers presented at the IV Conference on ``Dynamics'', Control and Applications to Applied Engineering and Life Science. The aim of this Special Issue is to collate original research articles that focus on the recent theoretical, computational, and experimental results in the field of nonlinear dynamics focusing on different engineering applications.
pp. 109-121 | DOI: 10.5890/JVTSD.2025.06.002
Diego Orlando, Paulo B. Gon¸calves, Stefano Lenci, Giuseppe Rega
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Stay cable systems present a complex nonlinear behavior under static and dynamic loads. The prevention of buckling and undesirable nonlinear vibrations of these structures is a major concern in engineering design. In this paper the stability analysis of a simplified two-degree-of-freedom model of a guyed tower is studied. The results show that the system displays a strong modal coupling, resulting in several unstable post-buckling solutions, thus leading to high imperfection sensitivity. For applied loads lower than the theoretical buckling load, the system is supposedly in a safe position, according to the classical theory of elastic stability. However, this is not completely true. The system may buckle at load levels much lower than the critical value due to the simultaneous effects of imperfections and dynamic disturbances. For systems liable to unstable post-buckling behavior, the safe pre-buckling well is bounded by the manifolds of the saddles associated with the unstable post-buckling paths. Here, the homoclinic orbits emerging from these saddles define the safe region. The geometry and size of the safe region is here analyzed using the mathematical methods of classical mechanics, in particular Lagrangian or Hamiltonian mechanics and numerical tools for nonlinear vibrations such as bifurcation diagrams, stability boundaries and basins of attraction. This is a first step in the evaluation of the integrity of the real dynamical system.
pp. 123-133 | DOI: 10.5890/JVTSD.2025.06.003
Mikhail E. Semenov, Olga O. Reshetova, Peter A. Meleshenko, Sergei V. Borzunov, Olesya I. Kanishcheva
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In this article we consider the van der Pol oscillator under hysteresis. In this case there are some peculiarities of the dynamics.
We propose a mathematical model that describes the dynamics of a modified van der Pol oscillator with a hysteresis block. In the modified model the quadratic term is replaced by a hysteresis block formalized within the Preisach model. A comparative analysis of the numerical results for the constructed model and the classical van der Pol oscillator is carried out. It is established that chaotic behavior can occur in the modified model unlike the classical case. We also consider a similar model under external excitation. Using the small parameter method, a solution is found, and a comparison of the obtained analytic and numerical results is made. A comparative analysis with the classical forced van der Pol oscillator model is also carried out.
pp. 135-146 | DOI: 10.5890/JVTSD.2025.06.004
Gabriella de O. M. Silva, Mauricio A. Ribeiro, Jose Manoel Balthazar, Jeferson J. de Lima, Cristhiane Goncalves, Vinicius Piccirilo, Marcus Varanis, Clivaldo de Oliveira, Angelo M. Tusset
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In this paper, we examined the nonlinear dynamic behavior of the coupling interactions between three oscillators that describe the regions of the human heart responsible for electrical impulses. Specifically, we focused on the sinoatrial node, the atrioventricular node, and the Purkinje complex. The dynamics of cardiac behavior can be effectively represented by a nonlinear dynamic model, such as the Van der Pol Oscillator. However, we added an external force described by Bessel functions applied to oscillators with non-ideal characteristics to explore the system's behavior further. Consequently, we analyzed the range of frequencies that alter the dynamic behavior of the system. To diagnose the nonlinear dynamic behavior, we employed classic tools such as the Lyapunov exponent, which established the convergence of trajectories, and the bifurcation diagram that confirms the periodic windows of the system and the phase space. Our findings enabled us to reconstruct an approximation of the Electrocardiogram (ECG) for a set of parameters, owing to the applicability of the mathematical model analyzed in the field of biomedical engineering.
pp. 147-158 | DOI: 10.5890/JVTSD.2025.06.005
Youssef El Moussati, Mustapha Hamdi, Mohamed Belhaq
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This paper investigates energy harvesting (EH) using simultaneous galloping and vortex-induced vibrations in a two-degree-of-freedom (2DOF) mechanical system coupled to an electrical circuit through an electromagnetic mechanism mounted on the secondary structure of the system. The main bluff body beam is subjected to aerodynamic forces, while the secondary beam is enclosed within the bluff body. The study compares two configurations. In the first configuration, the primary structure (with a bluff body) is submitted to a galloping aerodynamic force. In the second configuration, the primary structure is exposed simultaneously to galloping and vortex aerodynamic forces.
The harmonic balance method (HBM) is applied to approximate the amplitude of vibrations and output power for the two configurations. Numerical simulations are performed to validate the analytical results.
The energy harvested from both configurations is calculated and compared. The results show that combining galloping and vortex-induced vibrations enables the system to harvest higher energy at low wind speeds.
This result may provide an optimization process that can be used to supply some guidelines in the design of galloping and vortex-induced vibrations-based electromagnetic energy harvesters.
pp. 159-168 | DOI: 10.5890/JVTSD.2025.06.006
Angelo M. Tusset, Jose M. Balthazar, Marcos Goncalves, Maria E. K. Fuziki, Giane G. Lenzi
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This paper presents a control strategy of a parametrically excited pendulum with hyperchaotic behavior. It is considered that the pendulum is on a base subject to oscillation like the waves, thereby generating pitch and vertical movements at the base. We have formulated a control to suppress the chaotic behavior of the pendulum. The control strategy involves the application of two control signals: a nonlinear feedforward control to maintain a desired periodic orbit and a state feedback control to bring the system trajectory into the desired periodic orbit. State-Dependent Riccati Equation (SDRE) control is considered for obtaining the state feedback control. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and the effectiveness of the proposed active control.
pp. 169-177 | DOI: 10.5890/JVTSD.2025.06.007
Kaio C. B. Benedetti, Paulo B. Goncalves, Stefano Lenci, Giuseppe Rega
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The symmetric Duffing oscillator is well studied in literature and may describe a plethora of events in sciences and engineering, including systems with one or two potential wells. However, in many applications ranging from quantum physics to engineering, a symmetry-breaking effect described by a quadratic nonlinear term is an important feature, and the magnitude of the quadratic term is often unknown. Here the influence of a nondeterministic quadratic term on the global dynamics of a Duffing oscillator with a double potential well is investigated. To this end, the Adaptative Ulam Method is employed, refining the complex basins' boundaries and allowing the analysis of nondeterministic effects. Depending on the forcing magnitude and frequency, the system may exhibit intra or cross-well periodic, quasi-periodic, or chaotic motions.
pp. 179-186 | DOI: 10.5890/JVTSD.2025.06.008
Mauricio A. Ribeiro, Pamela Rafaela Martins, Daniel Felipe Meurer, Hilson Henrique Daum, Angelo M. Tusset, Jose Manoel Balthazar
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We investigate the behavior of basins of attraction and the nonlinear dynamics of an oscillator described in complex variables. To do this, we analyze the basin entropy and the uncertainty coefficient, establishing whether the attraction basins have the sieve phenomena. Another analysis carried out was with the Lyapunov exponent, which described the chaotic regions in which the oscillator is present. Thus, we were able to diagnose the behavior of the trajectories in phase space. As a result, we determined the set of parameters for Poincar茅 maps with their respective initial conditions. Such analyses corroborate future work involving control design to suppress chaotic behavior.
pp. 187-208 | DOI: 10.5890/JVTSD.2025.06.009
Bin Wu, Sifu Luo, C Steve Suh
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Understanding the mechanisms of propagation in complex networks is critical for various domains such as epidemiology, social media, communication networks, and multi-robot systems. This paper provides a comprehensive review of propagation models in complex networks, ranging from traditional deterministic models to advanced data-driven and deep learning approaches.
We first discuss static and dynamic network structures, noting that static models offer foundational insights into network behavior, while dynamic models capture the time-evolving nature of real-world systems. Deterministic models, such as the SIR framework, provide clear mathematical formulations for describing the spread of information and viruses, but they often lack flexibility in dealing with real-world randomness.
In contrast, stochastic models introduce randomness, making simulations of network behaviors more realistic, albeit at the expense of interpretability. Behavior-based models, including agent-based simulations, focus on individual decision-making processes, offering greater flexibility but requiring significant computational resources. Data-driven approaches leverage large datasets to adapt to changing network environments, improving accuracy in nonlinear and dynamic scenarios. These approaches can rely on the aforementioned models or be based on model-free machine learning methods.
We then explore supervised learning methods that require large amounts of labeled data, and unsupervised learning methods, which do not rely on labeled data. These two methods are the most mainstream approaches in machine learning. Building on this, we further investigate reinforcement learning, a newer learning paradigm that interacts with environments and does not require datasets.
Finally, we specifically discuss the application of graph neural networks (GNNs), which are closely aligned with network problems and have achieved revolutionary progress in modeling and optimizing propagation capabilities in large-scale and complex networks. The paper highlights key applications and challenges for each model type and emphasizes the growing role of hybrid and machine learning-based models in solving modern network propagation problems.
