Vol. 8, No. 2 (2024): Regular Issue

This is a review paper on the main theories of orbital mechanism that support the spiral arms in the case of grand design galaxies as well as in the case of barred spiral galaxies. While, in the first case stable periodic orbits form families of precessing ellipses that produce spiral density waves similar to those observed in real grand design galaxies, in the second case the spiral structure is supported by sticky chaotic orbits along unstable asymptotic manifolds. This mechanism is valid in the case of one pattern speed as well as of two different pattern speeds, for the bar and the spiral structure. Finally, in the case where the bar rotates much faster than the spiral arms, perturbed precessing ellipses can support spiral density waves.

The appearance of topological defects in the solid state is well observed and studied with the Kibble Zurek mechanism. However, the size of the systems and the effect that size has on the defect density is not yet properly studied and understood, as it is a problem of mathematical complexity. In this work, a number of simulations will be performed in order to see how the system's size affects the statistics of defects for different cooling rates. We have found that strange behaviors arise for specific sizes and cooling rates, which might hint at the existence of a correlation between the size and the defects. We also simulated the system for a variety of random flight sizes, in order to more accurately find the divergent behaviour and under which conditions it appears.

An updated YOLOv5s algorithm for vehicle and pedestrian identification is proposed to address the variety of vehicle and pedestrian targets in road traffic under complex environments. First, the network's nonlinear capability is improved with the addition of the GELU activation function; Second, the hybrid pyramid pooling structure (HSPPF) is utilized in the backbone network to lessen the loss of feature layer information; Finally, transfer learning and the EIoU loss function are incorporated to enhance the model's accuracy and speed of convergence. The experimental findings demonstrate that the enhanced algorithm can reliably identify targets such as vehicles and pedestrians. Its mAP value is 94.0%, 1.8% faster than before the enhancement, and its detection speed is 80.6 FPS. It is more suited for complex real-world traffic circumstances and has higher detection accuracy and speed when compared to other algorithms.

In this work, a memristor-based modified Cubic mapping model is presented by coupling a discrete memristance function with a modified Cubic map. This model is based on the memristor, which was discovered by Chua in 1971, as the fourth fundamental electrical component in addition to resistance, capacitance, and inductance. To investigate system's dynamical behavior a set of nonlinear tools has been used, such as bifurcation and maximal Lyapunov exponent diagrams as well as phase portraits. Interesting phenomena related to nonlinear theory have been observed such as, hyperchaotic behavior, regular (periodic and quasiperiodic) and chaotic orbits, as well as route to chaos through the mechanism of period doubling and crisis phenomena.

One of the frequent tasks in the robotic research field is to control the position of the robot and then change its current position to the intended state. This study focuses on the position feedback control through a state-feedback control law of an underactuated Lagrangian-type robotic system, called the inertia wheel inverted pendulum (IWIP), to its unstable upright state. Furthermore, using a rescaled dynamic model that describes the difference between the nonlinear dynamics and its approximate linear model, and based on the S-procedure, the Young inequality and the Schur complement lemma, we develop conditions on the feedback gain for the stabilization using two different methodologies. These designed methodologies are realized based on the Linear Matrix Inequality (LMI) techniques. We show that an initially obtained bilinear matrix inequality is converted into an LMI via some mathematical tools. Moreover, we introduce some further LMIs in order to minimize the feedback gain's size. Finally, we show some numerical results to illustrate the effectiveness of the proposed state-feedback control law for stabilizing the underactuated IWIP.

Biophysiological measurements are inadequate in making explicit the various properties of the brain at the network level for the reasons that these properties are complex functions of the electrochemical gradient and the cumulative area of triggered ion channels. Neuron dynamics, synaptic dynamics, and neural electrophysiological coupling have been considered in [1]. This study continues the work presented in [1] and considers biophysiological (local) and brain network (global) dynamics. The general framework for dynamic complex networks [2] is followed to describe brain network dynamics in this study. At the local level, individual neuron dynamics is defined using energy by considering each neuron as a type of biological battery. The potential energy is the charge of ions a neuron holds which is the membrane potential. The kinetic energy is the change of ion charge in time introduced by the ion flux across the membrane that induces the change of membrane potential. Degree-of-couplings, DOC k and DOC J, are indicators of the coupling strength of connected neurons. Since the energies of individual neurons in the network are normally distributed, brain network dynamics can be described by information entropy as a function of the probability of the individual neuron energies at the global level. Information entropy is also used to measure the degree of synchronization of the firing of action potential.

The effects of a distributed delay on a parametrically forced Van der Pol limit cycle oscillator are considered. Delays modeling time lags due to a variety of factors in self-excited systems, have been considered earlier in the context of modification and control of limit cycle and quasiperiodic responses. Those studies are extended here to include the effects of periodically amplitude modulated distributed delays in both the position and velocity. A normal form or 'slow flow' is employed to search for various bifurcations and transitions between regimes of different dynamics, including amplitude death and quasiperiodicity. The existence of quasiperiodic solutions then motivates the derivation of a second slow flow. A detailed comparison of the results and predictions from the second slow flow to numerical solutions is made. The second slow flow is also employed to approximate the amplitudes of the quasiperiodic solutions, yielding close agreement with the numerical results on the original system. Finally, the effect of varying the delay parameter is briefly considered, and the results and conclusions are summarized.