Cesar Manchein

We uncover the global organization of resonance structures in a periodically driven FitzHugh–Nagumo neuron model. High-resolution Lyapunov diagrams with local-maxima (LM) classification expose a hierarchical network of Arnold tongues in parameter space. Frequency-locking regions emerge from quasiperiodic dynamics and extend into chaotic domains, following a period-adding organization consistent with Farey-tree ordering. Successive magnifications reveal multiscale embeddings of stable periodic structures containing quint points, where five periodic domains coalesce and satisfy local LM-adding relations. Basin-of-attraction analysis confirms multistability, including coexistence of periodic and chaotic attractors. In a neurostimulation context, these results show that periodic forcing can induce multiple coexisting frequency-locked firing regimes with distinct LM counts, providing a dynamical basis for stimulus-dependent neural encoding and selective response modulation.

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.

We investigate the ratchet current (RC) in an inertial Brownian particle under the variation of mass, driving parameters, ratchet asymmetry, and temperature, modeled via the noise intensity (Q). Using stochastic simulations combined with parameter-space analysis, we show that the RC is strongly influenced by dynamical regimes, including periodic motion, chaos, bifurcations, and, most important, multistability. Notably, multistability plays a central role in the generation of temperature-induced RCs. The inclusion of Gaussian noise with arbitrarily small values of Q triggers transitions between coexisting deterministic attractors, leading to a preference for specific states. This noise-induced selection mechanism breaks velocity-space symmetry and enables directed transport. Lyapunov spectra, basins of attraction, and trajectory comparisons confirm that multistable regimes are the fundamental source of RC induced by noise. A global temperature analysis further reveals minimal RC at low Q, enhancement at intermediate Q, and suppression at high Q, while positive directed transport persists for small particle masses. These findings highlight the critical role of noise-driven transitions in deterministic multistable systems as a mechanism for controlling stochastic transport.

We investigate a novel nonautonomous dynamical system derived from the van der Pol oscillator by introducing a sinusoidal forcing term and a cubic nonlinearity. The resulting model is governed by two first-order differential equations with six parameters. We explore its behavior in the parameter plane defined by the amplitude and frequency of the forcing term. Dynamical characterization is performed using the largest Lyapunov exponent and the number of local maxima per period of a system variable. Our results reveal regions of multistability with coexisting periodic and chaotic attractors, as well as the presence of quart and quint points indicating parameter values where four or five distinct periodicities coalesce. Moreover, we identify organized periodic structures such as shrimp-like patterns in chaotic domains and Arnold tongue-like structures embedded in quasi-periodic domains, highlighting the system’s complex dynamics.

This paper investigates unbiased directed transport, known as the ratchet effect, within a system coupled to a fluid modeled by the bailout embedding technique. The system dynamics under the fluid influence are described by a four-dimensional mapping governed by parameters such as dissipation ([ ]), ratchet kicking (K), and the relationship between fluid and particle densities ([ ]). We explore the behavior of the Ratchet Current (RC) in the parameter spaces [ ] and [ ], particularly focusing on the aerosol case ([ ]). Our findings reveal a complex interplay of parameters, with larger RCs observed for parameter pairs that induce periodic dynamics in the ratchet system. Furthermore, we observe RC reversal as a function of [ ] and [ ], and identify coexisting attractors (multistability) at higher [ ] values. These results shed light on the intriguing phenomenon of directed transport in fluid dynamics, offering insights that may contribute to understanding particle transport in nature, especially in the aerosol regime.

In this paper, we investigate a seven-parameter, five-dimensional dynamical system, specifically a unidirectional coupling of two FitzHugh–Nagumo neuron models, with one neuron being sinusoidally driven. This master–slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes. The primary objective is to explore how the dynamics of the master neuron N1 influence the coupled system’s behavior. To achieve this, we generated cross sections of the seven-dimensional parameter space, known as parameter planes. Our findings reveal that in the periodic regime of N1, the coupled system exhibits period-adding sequences of Arnold tongue-like structures in the parameter planes. Furthermore, regions of multistability can also be identified in these parameter planes of the coupled system. In the quasiperiodic regime, regions of periodic motion are absent, with only regions of quasiperiodic and chaotic dynamics present. In the chaotic regime of N1, the parameter planes display regions of chaos, hyperchaos, and transient hyperchaos.

We investigate a monolayer graphene chip’s relativistic ratchet current (RRC). Our findings indicate that thermal noise can paradoxically amplify the RRC, in contrast to its conventional inhibitory role. Under noise, temperature (T) activation of the RRC remains stable over a broader range of T values, and an increased number of RRCs reversals are observed as a function of T and relevant parameters of the external electric field. The results regarding structural changes and symmetry breaking of the dissipative attractors can be understood. The observed activation and reversal of RRCs under a variation of external parameters unveil the diverse and complex behavior of the charge carrier transport on the graphene chip. Understanding this behavior allows for generating specific RRCs values, properties and effects for the charge carriers, offering a variety of possibilities for application and control of the graphene chip device.