Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting (...) attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated. (shrink)

Introduction 1. Methodological concerns 2. The Modulation of Being 3. The semantics of modulation of being 4. Mental Being 5. Reality and the Circle of being. Conclusion.

Here, a novel conservative chaotic oscillator is presented. Various dynamics of the oscillator are examined. Studying the dynamical properties of the oscillator reveals its unique behaviors. The oscillator is multistable with symmetric dynamics. Equilibrium points of the oscillator are investigated. Bifurcations, Lyapunov exponents, and the Poincare section of the oscillator’s dynamics are analyzed. Also, the oscillator is investigated from the viewpoint of initial conditions. The study results show that the oscillator is conservative and has no dissipation. It also has various (...) dynamics, such as equilibrium point and chaos. The stability analysis of equilibrium points shows there are both stable and unstable fixed points. (shrink)

This is the first reliable biography of Mulla Sadra Shirazi that examines his influences and legacy and includes an extensive survey of his work.

Megastable chaotic systems are somehow the newest in the family of special chaotic systems. In this paper, a new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. The introduced two-dimensional system has no defined equilibrium point. However, it seems that the origin plays the role of an unstable equilibrium point. Therefore, the attractors are determined as hidden attractors. Adding a forcing term to the system, we can obtain chaotic solutions (...) and coexisting strange attractors. Moreover, the effect of three different values of the forcing term’s amplitude is studied. The dynamical properties of the designed system are investigated using attractor plots, bifurcation diagrams, and Lyapunov Exponents diagram. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are also presented. (shrink)

The efficiency of distribution networks is hugely affected by active and reactive power flows in distribution electric power systems. Currently, distributed generators (DGs) of energy are extensively applied to minimize power loss and improve voltage deviancies on power distribution systems. The best position and volume of DGs produce better power outcomes. This work prepares a new hybrid SSA–GWO metaheuristic optimization algorithm that combines the salp swarm algorithm (SSA) and the gray wolf optimizer (GWO) algorithm. The SSA–GWO algorithm ensures generating the (...) best size and site of one and multi-DGs on the radial distribution network to decrease real power losses (RPL) (kW) on lines and resolve voltage deviancies. Our novel algorithm is executed on IEEE 123-bus radial distribution test systems. The results confirm the success of the suggested hybrid SSA–GWO algorithm compared with implementing the SSA and GWO individually. Through the proposed SSA–GWO algorithm, the study decreases the RPL and improves the voltage profile on distribution networks with multiple DGs units. (shrink)

This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is (...) revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters’ sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system’s attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator’s time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system. (shrink)

Dynamical analysis, chaos suppression and electronic implementation of the synchronous reluctance motor without external inputs are investigated in this paper. The different dynamical behaviors found in the SynRM without external inputs are illustrated in the two parameters largest Lyapunov exponent diagrams, one parameter bifurcation diagram, and phase portraits. The three single controllers are designed to suppress the chaotic behaviors found in SynRM without external inputs. The three proposed single controllers are simple and easy to implement. Numerical simulation results show that (...) the three proposed single controllers are effective. Finally, the dynamical behaviors found in the SynRM without external inputs and the physical feasibility of the three proposed single controllers are validated through circuit implementation on OrCAD-PSpice software. (shrink)

The debate between Mencius 孟子 (c. 372-c. 289 B.C.) and his contemporary, Gaozi 告子, regarding the theme of ren nei yi wai 仁內義外 (internal compassion versus external propriety) in the Mencius has alwa...

The three Nubian kingdoms that eventually emerged after the disintegration of Meroe, Noubadia, Makuria and Alodia (Alwa), first enter Byzantine historiography with the dramatic story of their conversion into Christianity told by John of Ephesus in the third part of his Church History, composed about AD 578–588 in Syriac. To be more exact, what John tells us is that, through the initiative of Empress Theodora, the Noubades and Alodians were converted into the Monophysite or (more specifically) Miaphysite creed, while the (...) Makurians remained hostile to the missionaries (later, apparently, to emerge as Dyophysites). RICHTER (R.) takes John's account as his point of departure, devoting half the book to a translation of the relevant chapters (IV.6–10 and 49–53) and a thorough discussion of their historical contents. It is the particular merit of his book, however, that he also comes to grips with the archaeological, especially architectural and epigraphic evidence on the Christianization process that surveys and excavations brought forth in the last century. The other half of the book brings together and systematizes such material from a great variety of secondary sources. The intense archaeological activities prompted by the flooding of vital parts of Lower Nubia have tended to give material remains precedence over literary witnesses in the current rewriting of Nubian history; R. endeavours to redress the balance, with regard to the sixth and seventh centuries, by juxtaposing the textual and archaeological sources. (shrink)