From a numerical simulation viewpoint, three numerical techniques having first order convergence have been employed to illustrate the numerical results obtained.In this paper, we investigate theoretically the potential of a nanoelectromechanical suspended beam resonator excited by two-external frequencies as a hardware random number generator. This system exhibits robust chaos, which is usually required for practical applications of chaos. Taking advantage of the robust chaotic oscillations, we consider the beam position as a possible random variable and perform tests to check its randomness. The beam position collected at fixed time intervals is used to create a set of values that is a candidate for a random sequence of numbers. To determine how close to a random sequence this set is, we perform several known statistical tests of randomness. The performance of the random sequence in the simulation of two relevant physical problems, the random walk and the Ising model, is also investigated. RO4929097 mouse An excellent overall performance of the system as a random number generator is obtained.We study a single cubic complex Ginzburg-Landau equation with nonlinear gradient terms analytically and numerically. This single equation allows for the existence of stable dissipative solitons exclusively due to nonlinear gradient terms. We shed new light on the feedback loop, leading to dissipative solitons (DSs) by analyzing a mechanical analog as a function of the magnitude of the amplitude. In addition, we present analytic results incorporating four nonlinear gradient terms and derive necessary conditions for the existence of DSs. We also elucidate in detail for the case of the Raman contribution the scaling behavior for the limit of the vanishing Raman term.This paper researches the dynamic snap-through phenomena and the coexistence of the multi-pulse jumping chaotic dynamics in bistable equilibrium positions and the large amplitude nonlinear vibrations for a simply supported buckled 3D-kagome truss core sandwich rectangular plate under combined transverse and in-plane excitations based on the extended high-dimensional Melnikov method. According to the two-degree-of-freedom non-autonomous nonlinear dynamical system of the buckled truss core sandwich rectangular plate and the theory of normal form, it is found that some nonlinear terms have less effects on the nonlinear dynamic responses than other nonlinear terms. The extended high-dimensional Melnikov method is employed to investigate the dynamic snap-through phenomena and the bistable multi-pulse jumping chaotic vibrations around the upper-mode and the lower-mode for two different cases of buckling in the truss core sandwich rectangular plate. A numerical method is used to detect the bistable multi-pulse jumping chaotic vibrations around two stable equilibrium positions for the non-autonomous buckled truss core sandwich rectangular plate. The obtained theoretical and numerical results indicate that there exists the coexistence of the bistable multi-pulse jumping chaotic vibrations and the large amplitude nonlinear vibrations in the buckled truss core sandwich rectangular plate under combined transverse and in-plane excitations.This paper presents a novel memristor-based dynamical system with circuit implementation, which has a 2×3-wing, 2×2-wing, and 2×1-wing non-Shilnikov type of chaotic attractors. The system has two index-2 saddle-focus equilibria, symmetrical with respect to the x-axis. The system is analyzed with bifurcation diagrams and Lyapunov exponents, demonstrating its complex dynamical behaviors the system reaches the chaotic state from the periodic state through alternating period-doubling bifurcations and then from the chaotic state back to the periodic state through inverse bifurcations, as one parameter changes. It shows two interesting phenomena a jump-switching periodic state and jump-switching chaotic state. Also, the system can sustain chaos with a constant Lyapunov spectrum in some initial conditions and a parameter set. In addition, a class of symmetric periodic bursting phenomena is surprisingly observed under a particular set of parameters, and its generation mechanism is revealed through bifurcation analysis. Finally, the circuit implementation verifies the theoretical analysis and the jump-switching numerical simulation results.We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that form the second layer. The nonlocality in the interaction among the dynamic agents in the second layer induces different types of chimera-related dynamical states in the first layer. The amplitude chimeras developed in them are found to be extremely stable, while chimera death states are prevalent for increased coupling strengths. The results presented are for a system of coupled Stuart-Landau oscillators and can, in general, represent systems with short-range interactions coupled to another set of systems with long-range interactions. In this case, by tuning the range of interactions among the oscillators or the coupling strength between two types of systems, we can control the nature of chimera states and the system can also be restored to homogeneous steady states. The dynamic agents interacting nonlocally with long-range interactions can be considered as a dynamic environment or a medium interacting with the system. We indicate how the second layer can act as a reinforcement mechanism on the first layer under various possible interactions for desirable effects.Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier studies of extreme events on complex networks had focused only on the nodal events. If random walks are used to model the transport process on a network, it is known that degree of the nodes determines the extreme event properties. In contrast, in this work, it is shown that extreme events on the edges display a distinct set of properties from that of the nodes. It is analytically shown that the probability for the occurrence of extreme events on an edge is independent of the degree of the nodes linked by the edge and is dependent only on the total number of edges on the network and the number of walkers on it. Further, it is also demonstrated that non-trivial correlations can exist between the extreme events on the nodes and the edges. These results are in agreement with the numerical simulations on synthetic and real-life networks.