Search Results (53)

This study develops a nonlinear dynamic model of a human-inspired electromechanical arm system subjected to high loads. The proposed simplified representation preserves essential nonlinear dynamics using a reduced number of generalized coordinates. The model is represented by an electromechanical analog comprising a DC motor, a transmission system, and a multi-degree-of-freedom mechanical structure. The formulation is based on Lagrangian mechanics and accounts for inertia, damping, stiffness, and nonlinear kinematic coupling induced by joint misalignment. The numerical results were assessed using a consistency-based verification approach with several independent nonlinear analysis tools. The Lyapunov exponent was used in conjunction with bifurcation diagrams, Poincaré maps, and FFT spectra to identify the transition from stable operation to chaotic behavior as the external load increased. The results reveal a progressive transition from periodic motion to quasi-periodic oscillations and chaotic regimes, with fully developed chaotic behavior emerging for loads exceeding approximately 35 kg. Analysis of the Lyapunov exponent supports this interpretation, indicating stable, quasi-critical, or chaotic regimes depending on the sign of λ_max. The concordance among these independent indicators provides numerical verification of the observed stability transitions. The control gain significantly influences energy dissipation and system stability. The proposed model provides a reduced-order framework for studying nonlinear stability phenomena in human-inspired electromechanical systems. Potential applications involve rehabilitation devices and safety studies of human–robot interactions. Full article

The study investigates the nonlinear dynamics of a harmonically excited Duffing oscillator coupled with an unforced two-degrees-of-freedom nonlinear energy sink. The external excitation is applied only to the primary oscillator; meanwhile, the NES response is induced through nonlinear internal coupling. The governing nonlinear ordinary differential equations are analyzed using the proposed non-perturbation approach, which does not rely on small-parameter assumptions or Taylor-series expansions. The formulation is used to obtain amplitude-dependent equivalent linear representations and analytical approximations of the coupled system. The analytical results are compared with direct numerical simulations, showing overall agreement with the full nonlinear model. The stability of the steady-state solutions is examined under variations of the main system parameters. The results indicate that the nonlinear coupling and stiffness parameters significantly affect the response amplitudes, stability characteristics, and overall dynamical behavior. Additional analyses using bifurcation diagrams, Lyapunov exponents, Poincaré maps, and basins of attraction reveal transitions between periodic, quasi-periodic, and chaotic regimes, as well as the presence of multi-stability and sensitivity to initial conditions. The proposed framework provides a useful analytical tool in studying the dynamics and stability of nonlinear oscillatory systems over a wide range of operating conditions. Full article

This work examines how well a Negative Derivative Feedback (NDF) controller suppresses vibration in a nonlinear electromechanical oscillator that is subjected to mixed excitations. Coupled nonlinear ordinary differential equations are used to model the system and show how mechanical and electrical components interact. The method of multiple scales (MMS) is used to develop analytical approximate solutions up to the second order, specifically for the primary resonance scenario. This study’s main contribution is a thorough bifurcation analysis and proof of the NDF controller’s high efficacy, which effectively lowers the first and second mode resonance amplitudes by roughly $99.8\%$ and $98\%$., respectively, with impressive reported effectiveness values of roughly 590 and 51.5. Additionally, the quantitative error analysis between the numerical simulation and the analytical approximation solution demonstrates a high degree of agreement, with a maximum error of less than ${10}^{-5}\%$ for the second mode and just $0.01\%$ for the first mode. Furthermore, we present the impact of parameters on FRCs. Frequency response curves (FRCs) are used in a thorough comparison analysis to assess the behavior of the system both before and after the controller is activated. A strong degree of connection between the analytical conclusions and numerical simulations carried out using the “fourth-order Runge–Kutta method” rigorously validates the accuracy of the perturbation analysis. Additionally, a performance benchmark between different control techniques, such as the NDF controller, Positive Position Feedback (PPF), and Linear Negative Position Feedback (LNPF), is shown in the paper. When compared to alternative approaches, the NDF controller shows the greatest reduction in oscillation amplitudes and higher robustness, as shown by transient response analysis (time history) at various time intervals. The outcomes validate the NDF approach’s dependability and efficiency in stabilizing intricate nonlinear electromechanical systems. The chaotic response and system periodicity were demonstrated through bifurcation diagrams and Poincaré maps. Full article

Flow-induced self-excited vibration may exhibit high-frequency numerical oscillations and chaotic-like responses in long-duration simulations due to strong nonlinearity and multimodal coupling. In this study, a two-node cable finite element model incorporating torsional degrees of freedom, nonlinear aerodynamic forces, and geometric nonlinearity is developed to evaluate the long-term computational performance of the Newmark average acceleration method and the Bathe composite integration scheme. Simulations are conducted for weakly nonlinear, transitional nonlinear, and near 1:1 internal resonance regimes. The results show that, as the degree of nonlinearity increases, the Newmark method produces more pronounced non-principal high-frequency components, a more scattered distribution of Poincaré points, and larger deviations from the expected principal-mode-dominated beating response. These observations indicate that, under the present model and discretization conditions, the chaotic-like response obtained by the Newmark method is strongly affected by non-principal high-frequency contamination. In contrast, the response computed by the Bathe method remains stably governed by the two dominant frequencies associated with the near-resonant beating mechanism. The results indicate that, for the long-duration nonlinear galloping problems considered in this study, appropriate algorithmic dissipation can reduce non-principal high-frequency disturbances and improve the interpretability of the numerical results. Full article

Hysteretic nonlinear vibration systems can exhibit jumps, coexisting attractors, and strong dependence on the initial state, particularly when material hysteresis is coupled with geometric nonlinearity. This paper investigates the global nonlinear dynamics of a harmonically forced single-degree-of-freedom oscillator incorporating pseudoelastic shape memory alloy (SMA) wires in a perpendicular geometric configuration. Cyclic force–displacement tests on pseudoelastic SMA wires are used to calibrate the constitutive response, after which steady-state dynamics are analyzed using time integration, numerical continuation (COCO), and basin-of-attraction computations over representative excitation frequencies, pre-tension levels, and the number of wires. The calibrated model predicts rich response regimes including jump phenomena, coexisting stable solutions, multistability, asymmetric periodic responses, and the pronounced dependence of the achieved steady response on initial conditions and internal state. Basin computations reveal sensitive partitioning of the state space between competing attractors, highlighting the influence of the initial and internal state in oscillators that combine pseudoelastic hysteresis with geometric stiffening. Additional numerical exploration of a negative pre-tension extension indicates transitions to more complex responses, including quasi-periodic and chaotic behaviour, but these are presented as secondary results outside the directly validated tension-wire regime. The results clarify how calibrated SMA hysteresis and geometric nonlinearity jointly shape multistability and basin structure in pseudoelastic oscillators. Full article

We investigate the nonlinear dynamics of a linearly coupled van der Pol–Duffing system using numerical continuation, time-domain simulations, stochastic analysis, and analog circuit experiments. The model exhibits a rich variety of dynamical regimes, including periodic oscillations, period-doubling cascades, and chaotic attractors arising from the interplay between self-excitation and nonlinear stiffness. Numerical continuation is employed to reconstruct the bifurcation structure, enabling the identification of equilibrium branches, periodic solutions, and their stability in parameter space. The time-domain numerical results reveal the mechanisms governing transitions between regular and chaotic dynamics. To assess robustness under realistic conditions, intrinsic stochastic perturbations are introduced, showing that increasing noise intensity progressively erodes fine periodic structures, while larger dynamical domains remain comparatively robust. Experimental results obtained from an analog circuit implementation confirm the main dynamical regimes predicted numerically. Overall, the combined computational and experimental approach provides a systematic characterization of the system’s bifurcation structure and its robustness to noise. The results support the concept of chaos-based sensing and are consistent with previous findings in chaotic bioimpedance detection, indicating that maximum sensitivity occurs near regions of high bifurcation complexity, where small parameter variations induce significant qualitative changes in the system dynamics. Full article

This paper is devoted to the problem of identifying the mechanisms of hard excitation of oscillations in coupled systems of equilibrium neurons. In this study, a system of two coupled Chialvo neurons is used. For the deterministic model, we studied how increased coupling causes an abrupt transformation of the quiescent neurons into complex oscillations, both regular and chaotic. We show that even in the case when the deterministic system is in equilibrium, similar spike oscillations can be generated by noise. The important role of fractal basins of short and long deterministic transients is discussed. The potential of the principal directions and confidence domain methods for analyzing noise-induced excitation is demonstrated. The phenomena of coherence resonance and the global transition from order to chaos are explored. Full article

In this study, we develop and investigate a novel fractional discrete-time computer virus dynamics model in two dimensions with a memristive nonlinear coupling mechanism. The memristor introduces nonlinearity by having memory regulation that depends on the state and enhances the propagation dynamics of virus spread. By investigating both matching and non-matching fractional orders, it is then possible to derive useful knowledge with respect to cooperating roles in terms of fractional memory and memristive effects. The complexity behind it is confirmed via 3D phase portraits, bifurcation analysis with LE_max calculation, 0–1 chaos test, and SE complexity. Numerical results reveal rich dynamical phenomena, including periodic oscillations, quasi-periodicity, and strong chaos. In fact, positive LE_max values, Brownian-like trajectories, and high-complexity SE corroborate the chaotic nature of the regimes. Thereby, the fractional-order separation in noncommensurate conditions is a marker of chaotic motion, magnified in the emergently high-dimensional space introduced by the memristive element. As these results indicate that the derivative model proposed here provides an excellent fit for complex viruses present in scaffolds, it may prove to be a useful modeling tool. Full article

The Rössler system is a paradigmatic chaotic oscillator widely used to investigate synchronization phenomena. Existing studies on monovariate coupling almost exclusively rely on the x or y variables, while coupling through z is commonly regarded as ineffective. In this work, we report that complete synchronization through the z variable is indeed possible, provided that specific parameter values are chosen. We further consider a parameter regime in which the Rössler system exhibits multistability and show that synchronization via z-coupling occurs only when the dynamics evolve on a particular attractor. Although synchronization can be achieved, the admissible range of coupling strengths is very narrow as determined by the master stability function. For small networks, full connectivity is required, whereas larger networks can tolerate the removal of a limited number of links without losing synchronization. An analytical expression predicting the fraction of connections that must be preserved as a function of network size is derived and validated, revealing that a very high average degree is necessary. This effectively excludes common topologies such as small-world and scale-free networks. Numerical examples with up to 100 oscillators are presented, and potential challenges that may yield new insights are discussed. Full article

This paper investigates the dynamics of a permanent magnet synchronous motor (PMSM) and controls its chaotic speed behavior using the synergetic control technique (SCT). The model includes electrical dynamics in the dq frame and mechanical speed dynamics, with a scalar parameter $\gamma$ capturing cross-coupling effects. The equilibrium structure and local stability properties of the PMSM are analyzed. For zero input voltages and zero load torque, the system exhibits a pitchfork-type bifurcation in the electrical–mechanical equilibrium as $\gamma$ crosses a critical value. Explicit expressions are derived for all equilibria, and their stability is characterized using eigenvalue analysis and the Routh–Hurwitz criterion, and a secondary loss of stability via a Hopf-type mechanism is identified. The case of nonzero input voltages with zero load torque is also discussed. Numerical simulations confirm the analytical results and highlight the parameter regions that admit stable operation. Bifurcation diagrams show the different PMSM behaviors as the parameter $\gamma$ varies. For a certain interval of $\gamma$, the PMSM speed undergoes chaotic oscillations. The SCT is introduced to control the chaos. Macro variables are chosen to design the SCT. The derived SCT is implemented to eliminate the chaotic speed. The controller provides good performance in suppressing the chaos. The controller is tested under sudden reference speed change where the controller gets the new reference speed accurately. It is also evaluated under sudden and sinusoidal load torque variations. Full article

Cascade reservoir optimization faces significant challenges due to multi-dimensional, non-convex, and nonlinear characteristics with coupled constraints. As reservoir numbers increase, computational complexity escalates dramatically, limiting conventional optimization methods’ effectiveness. This paper proposes HHONMPA, a hybrid algorithm combining Harris Hawks Optimization (HHO) with Marine Predators Algorithm (MPA). The method uses SPM chaotic mapping for population initialization to enhance diversity and integrates both algorithms’ predatory behaviors. During exploration, it employs Brownian motion and improved Lévy flight strategies for global search, while exploitation uses enhanced HHO for local optimization. A novel Dual-Period Oscillation Attenuation Strategy dynamically adjusts parameters to balance exploration-exploitation. Performance validation using CEC2017 benchmark functions shows HHONMPA significantly outperforms the original HHO and MPA in solution accuracy and convergence speed, confirmed through statistical testing. Engineering validation applies the algorithm to the Lower Jinsha River—Three Gorges four-reservoir system, conducting experiments across various hydrological scenarios. Results demonstrate substantial improvements in search accuracy and convergence efficiency compared to existing methods. HHONMPA effectively addresses large-scale cascade reservoir optimization challenges, offering promising prospects for water resource management and hydropower scheduling applications. Full article

This study introduces a novel control strategy aimed at achieving projective synchronization in incommensurate fractional-order chaotic systems (IFOCS). The approach integrates the mathematical framework of fractional calculus with the recursive structure of the backstepping control technique. A key feature of the proposed method is the systematic use of the Mittag–Leffler function to verify stability at every step of the control design. By carefully constructing the error dynamics and proving their asymptotic convergence, the method guarantees the overall stability of the coupled system. In particular, stabilization of the error signals around the origin ensures perfect projective synchronization between the master and slave systems, even when these systems exhibit fundamentally different fractional-order chaotic behaviors. To illustrate the applicability of the method, the proposed fractional order backstepping control (FOBC) is implemented for the synchronization of two representative systems: the fractional-order Van der Pol oscillator and the fractional-order Rayleigh oscillator. These examples were deliberately chosen due to their structural differences, highlighting the robustness and versatility of the proposed approach. Extensive simulations are carried out under diverse initial conditions, confirming that the synchronization errors converge rapidly and remain stable in the presence of parameter variations and external disturbances. The results clearly demonstrate that the proposed FOBC strategy not only ensures precise synchronization but also provides resilience against uncertainties that typically challenge nonlinear chaotic systems. Overall, the work validates the effectiveness of FOBC as a powerful tool for managing complex dynamical behaviors in chaotic systems, opening the way for broader applications in engineering and science. Full article

Synchronization in complex networks mainly considers positive (attractive) couplings to guarantee network stability. However, in many real-world systems or processes, negative (repulsive) interactions exist, and this poses a challenging problem. In this proposal, we present an algorithm to design stable signed Laplacian matrices with mixed attractive and repulsive couplings that ensure stability in both complete and in-phase synchronization. The main result is established through a constructive theorem that guarantees a single zero eigenvalue, while all other eigenvalues are negative, thereby preserving the diffusivity condition. The algorithm allows control over the spectral properties of the matrix by adjusting two parameters, which can be interpreted as a pole placement strategy from control theory. The approach is validated through numerical examples involving the synchronization of a network of chaotic Lorenz systems and a network of Kuramoto oscillators. In both cases, full synchronization is achieved despite the presence of negative couplings. Full article

Natural dynamical systems can often display various long-term behaviours, ranging from entirely predictable decaying states to unpredictable, chaotic regimes or, more interestingly, highly correlated and intricate states featuring emergent phenomena. That, of course, imposes a level of generality on the models we use to study them. Among those models, coupled oscillators and cellular automata (CA) present a unique opportunity to advance the understanding of complex temporal behaviours because of their conceptual simplicity but very rich dynamics. In this contribution, we review the work completed by our research team over the last few years in the development and application of an alternative information-based characterization scheme to study the emergent behaviour and information handling of nonlinear systems, specifically Adler-type oscillators under different types of coupling: local phase-dependent (LAP) coupling and Kuramoto-like local (LAK) coupling. We thoroughly studied the long-term dynamics of these systems, identifying several distinct dynamic regimes, ranging from periodic to chaotic and complex. The systems were analysed qualitatively and quantitatively, drawing on entropic measures and information theory. Measures such as entropy density (Shannon entropy rate), effective complexity measure, and Lempel–Ziv complexity/information distance were employed. Our analysis revealed similar patterns and behaviours between these systems and CA, which are computationally capable systems, for some specific rules and regimes. These findings further reinforce the argument around computational capabilities in dynamical systems, as understood by information transmission, storage, and generation measures. Furthermore, the edge of chaos hypothesis (EOC) was verified in coupled oscillators systems for specific regions of parameter space, where a sudden increase in effective complexity measure was observed, indicating enhanced information processing capabilities. Given the potential for exploiting this non-anthropocentric computational power, we propose this alternative information-based characterization scheme as a general framework to identify a dynamical system’s proximity to computationally enhanced states. Furthermore, this study advances the understanding of emergent behaviour in nonlinear systems. It explores the potential for leveraging the features of dynamical systems operating at the edge of chaos by coupling them with computationally capable settings within machine learning frameworks, specifically by using them as reservoirs in Echo State Networks (ESNs) for time series forecasting and predictive modeling. This approach aims to enhance the predictive capacity, particularly that of chaotic systems, by utilising EOC systems’ complex, sensitive dynamics as the ESN reservoir. Full article