The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It shown that system can exhibit a {hidden attractor} case multistability as well classical {self-excited attractor}. hidden attractor this be localized by analytical-numerical methods based on {continuation} and {perpetual points}. For numerical study attractors' dimension concept {finite-time Lyapunov dimension} developed. A conjecture self-excited attractors notion {exact are discussed....

Amplitude death (AD) in hidden attractors is attained with a scheme of linear augmentation. This control capable stabilizing the system to fixed point state even when original does not have any point. Depending on parameter, different routes AD such as boundary crises and Hopf bifurcation are observed. Lyapunov exponent amplitude index used study dynamical properties system.

We study the dynamics of nonlinear oscillators under mean-field diffusive coupling. observe that this form coupling leads to amplitude death via a synchronization transition in parameter space strength and control parameter. A general criterion for any given dynamical system with diffusion is obtained, these transitions are characterized using various indices such as average phase difference, Lyapunov exponents, amplitude. This behavior analyzed plane by numerical studies specific cases...

In the field of complex dynamics, multistable attractors have been gaining significant attention due to their unpredictability in occurrence and extreme sensitivity initial conditions. Co-existing are abundant diverse systems ranging from climate finance ecological social systems. this article, we investigate a data-driven approach infer different dynamics system using an echo state network. We start with parameter-aware reservoir predict for parameter values. Interestingly, machine is able...

We investigate the dynamical evolution of Stuart-Landau oscillators globally coupled through conjugate or dissimilar variables on simplicial complexes. report a first-order explosive phase transition from an oscillatory state to oscillation death, with higher-order (2-simplex triadic) interactions, as opposed second-order only pairwise (1-simplex) interactions. Moreover, system displays four distinct homogeneous steady states in presence triadic contrast two observed dyadic calculate...

Higher-order interactions have been instrumental in characterizing the intricate complex dynamics a diverse range of large-scale systems. Our study investigates effect attractive and repulsive higher-order globally non-locally coupled prey–predator Rosenzweig–MacArthur Such lead to emergence spatiotemporal chimeric states, which are otherwise unobserved model system with only pairwise interactions. exhibits second-order transition from chimera-like state (mixture oscillating steady nodes)...

We propose a general strategy to stabilize the fixed points of nonlinear oscillators with augmented dynamics. By using this scheme, either unstable oscillatory system or new point can be stabilized. The Lyapunov exponents are used study dynamical properties. This scheme is illustrated chaotic Lorenz oscillator coupled through an external linear system. experimental demonstration proposed also presented.

Abstract We report the occurrence of an explosive death transition for first time in ensemble identical limit cycle and chaotic oscillators coupled via mean–field diffusion. In both systems, variation normalized amplitude with coupling strength exhibits abrupt irreversible to state from oscillatory this order phase is independent size system. This quite general has been found all systems where in–phase oscillations co–exist a dependent homogeneous steady state. The backward point calculated...

Abstract Most previous studies on coupled dynamical systems assume that all interactions between oscillators take place uniformly in time, but, reality, this does not necessarily reflect the usual scenario. The heterogeneity timings of such strongly influences processes. Here, we introduce a time-evolving state-space-dependent coupling among an ensemble identical oscillators, where individual units are interacting only when mean state system lies within certain proximity phase space. They...

We study the dynamics of oscillators that are coupled in relay; namely, through an intermediary oscillator. From previous studies it is known show a transition from in-phase to out-of-phase oscillations or vice versa when interactions involve time delay. Here we that, absence delay, relay coupling conjugate variables has same effect. However, this phase-flip does not occur abruptly at certain critical value parameter. Instead find parameter region around where bistability occurs. In interval...

We study the dynamics of nonlinear oscillators indirectly coupled through a dynamical environment or common medium. observed that this form indirect coupling leads to synchronization and phase-flip transition in periodic as well chaotic regime oscillators. The from in- anti-phase vise-versa is analyzed parameter plane with examples Landau-Stuart Rössler transitions are characterized using various indices such average phase difference, frequency, Lyapunov exponents. Experimental evidence...

The role of a new form dynamic interaction is explored in network generic identical oscillators. proposed design coupling facilitates the onset plethora asymptotic states including synchronous states, amplitude death oscillation mixed state (complete synchronized cluster and small unsynchronized domain), bistable (coexistence two attractors). dynamical transitions from oscillatory to are characterized using an average temporal approximation, which agrees with numerical results interaction. A...

Hidden attractors are present in many nonlinear dynamical systems and not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route these is still fully understood. In this Research Letter, we stable equilibrium points without any points. We show that emerge as a result saddle-node bifurcation unstable periodic orbits. Real-time hardware experiments were performed demonstrate existence systems. Despite...

Abstract Mechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due internal system parameters like stiffness and external forcing. Mapping out complete bifurcation diagrams numerically or experimentally is resource-consuming, even infeasible. This study uses a data-driven approach investigate how bifurcations can be learned few response measurements. Particularly, the concept of reservoir computing (RC)...

Real-world networks are often characterized by simultaneous interactions between multiple agents that adapt themselves due to feedback from the environment. In this article, we investigate dynamics of an adaptive multilayer network Kuramoto oscillators with higher-order interactions. The nodes within layers adaptively controlled through global synchronization order parameter adaptations present alongside both pairwise and We first explore a linear form adaptation function discover tiered...

In systems that exhibit multistability, namely those have more than one coexisting attractor, the basins of attraction evolve in specific ways with creation each new attractor. These multiple attractors can be created via different mechanisms. When an attractor is formed a saddle-node bifurcation, size its basin increases as power-law bifurcation parameter. weak dissipation, low-order periodic increase linearly, while high-order decay exponentially dissipation increased. general features are...