scholarly journals Asymmetry Evolvement and Controllability of a Symmetric Hyperchaotic Map

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1039
Author(s):  
Sixiao Kong ◽  
Chunbiao Li ◽  
Haibo Jiang ◽  
Yibo Zhao ◽  
Yanling Wang
Keyword(s):  
Numerical Simulation ◽  
Hardware Implementation ◽  
Trigonometric Function ◽  
Initial Condition ◽  
Trigonometric Functions ◽  
Negative Coefficient ◽  
Offset Boosting

Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation.

scholarly journals An Initial-Controlled Double-Scroll Hyperchaotic Map

2021 ◽  
Author(s):  
Yongxin Li ◽  
Chunbiao Li ◽  
Sicong Liu ◽  
Tengfei Lei ◽  
Yicheng Jiang
Keyword(s):  
Dynamical System ◽  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Initial Condition ◽  
Offset Boosting ◽  
Sine Functions ◽  
Sinusoidal Function

Abstract Initial condition-dominated offset boosting provides a special channel to arrange coexisting orbits. Due to the nonlinearity and inherent periodicity, sinusoidal function is often introduced into a dynamical system for multistability design. In this paper, an initial-controlled double-scroll hyperchaotic map is constructed based on two sine functions. Four patterns of the double-scroll hyperchaotic orbits are found as 0-degree, 90-degree, 45-degree and 135-degree. Consequently, different modes for attractor growing are demonstrated. Finally, hardware experiments based on STM32 are carried out to verify the theoretical analysis and numerical simulation.

Memristor Oscillators and its FPGA Implementation

2011 ◽  
Vol 383-390 ◽  
pp. 6992-6997 ◽  
Author(s):  
Ai Xue Qi ◽  
Cheng Liang Zhang ◽  
Guang Yi Wang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Field Programmable Gate Array ◽  
Chaotic Attractor ◽  
Hardware Implementation ◽  
Fpga Implementation ◽  
Experimental Results ◽  
Linear Resistance ◽  
Non Linear ◽  
Field Programmable

This paper presents a method that utilizes a memristor to replace the non-linear resistance of typical Chua’s circuit for constructing a chaotic system. The improved circuit is numerically simulated in the MATLAB condition, and its hardware implementation is designed using field programmable gate array (FPGA). Comparing the experimental results with the numerical simulation, the two are the very same, and be able to generate chaotic attractor.

Initial Condition and Calculation Method for the Numerical Simulation of LPE

2007 ◽  
Vol 40 (11) ◽  
pp. 928-938
Author(s):  
Hiromoto Susawa ◽  
Toshihiro Tsuji ◽  
Takashi Jimbo ◽  
Tetsuo Soga
Keyword(s):  
Numerical Simulation ◽  
Calculation Method ◽  
Initial Condition

Energy of a tsunami in the framework of an irreversible deformation of the ocean bottom

2020 ◽  
Author(s):  
Emile Okal ◽  
Costas Synolakis
Keyword(s):  
Numerical Simulation ◽  
Exact Analytical Solution ◽  
Source Area ◽  
Ocean Bottom ◽  
Generation Process ◽  
Initial Condition ◽  
Tsunami Simulation ◽  
Earthquake Sources ◽  
A Value ◽  
Classic Approach

<p>The classic approach to tsunami simulation by earthquake sources consists<br>of computing the vertical static deformation of the ocean bottom due to<br>the dislocation, using formalisms such as Mansinha and Smylie's [1971] or<br>Okada's [1985], and of transposing that field directly to the ocean's<br>surface as the initial condition of the numerical simulation.<br>We look into the limitations of this approach by developing a very<br>simple general formula for the energy of a tsunami, expressed as the<br>work performed against the hydrostatic pressure at the bottom of<br>the ocean, in excess of the simple increase in potential energy<br>of the displaced water, due to the irreversibility of the process.<br>We successfully test our results against the exact analytical solution<br>obtained by Hammack [1972] for the amplitude of a tsunami generated<br>by the exponentially-decaying uplift of a circular plug on the ocean<br>bottom. We define a "tsunami efficiency" by scaling the resulting energy<br>to its classical value derived, e.g., by Kajiura [1963]. As expected, we<br>find that sources with shorter rise times are more efficient tsunami<br>generators; however, an important new result is that the efficiency is<br>asymptotically limited, for fast sources, to a value depending on the<br>radius of the source, scaled to the depth of the water column; as this<br>ratio increases, it becomes more difficult to flush the water out of<br>the source area during the generation process, resulting in greater<br>tsunami efficiency. Fortunately, this result should not affect<br>significantly the generation of tusnamis by mega-earthquakes.</p>

A High-Resolution Modeling Study of the 24 May 2002 Dryline Case during IHOP. Part I: Numerical Simulation and General Evolution of the Dryline and Convection

2006 ◽  
Vol 134 (1) ◽  
pp. 149-171 ◽  
Author(s):  
Ming Xue ◽  
William J. Martin
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
High Resolution ◽  
Companion Paper ◽  
Horizontal Resolution ◽  
Initial Condition ◽  
Moist Convection ◽  
Convective Initiation ◽  
Deep Moist Convection ◽  
Localized Forcing

Abstract Results from a high-resolution numerical simulation of the 24 May 2002 dryline convective initiation (CI) case are presented. The simulation uses a 400 km × 700 km domain with a 1-km horizontal resolution grid nested inside a 3-km domain and starts from an assimilated initial condition at 1800 UTC. Routine as well as special upper-air and surface observations collected during the International H2O Project (IHOP_2002) are assimilated into the initial condition. The initiation of convective storms at around 2015 UTC along a section of the dryline south of the Texas panhandle is correctly predicted, as is the noninitiation of convection at a cold-front–dryline intersection (triple point) located farther north. The timing and location of predicted CI are accurate to within 20 min and 25 km, respectively. The general evolution of the predicted convective line up to 6 h of model time also verifies well. Mesoscale convergence associated with the confluent flow around the dryline is shown to produce an upward moisture bulge, while surface heating and boundary layer mixing are responsible for the general deepening of the boundary layer. These processes produce favorable conditions for convection but the actual triggering of deep moist convection at specific locations along the dryline depends on localized forcing. Interaction of the primary dryline convergence boundary with horizontal convective rolls on its west side provides such localized forcing, while convective eddies on the immediate east side are suppressed by a downward mesoscale dryline circulation. A companion paper analyzes in detail the exact processes of convective initiation along this dryline.

scholarly journals The simulation of the flow through the porous media and diffusible barriers

2018 ◽  
Vol 180 ◽  
pp. 02052
Author(s):  
Martin Kyncl ◽  
Jaroslav Pelant
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Fluid Flow ◽  
Compressible Fluid ◽  
Gas Flow ◽  
Initial Condition ◽  
Computational Results ◽  
Viscous Compressible Fluid ◽  
Compressible Fluid Flow ◽  
Flow Through

Here we work with the RANS equations describing the non-stationary viscous compressible fluid flow. We focus on the numerical simulation of the flow through the porous media, characterized by the loss of momentum. Further we simulate the flow through the set of diffusible barriers. Here we analyze the modification of the Riemann problem with one-side initial condition, complemented with the Darcy’s law and added inertial loss. We show the computational results obtained with the own-developed code for the solution of the compressible gas flow.

scholarly journals An Axiom of True Courses Calculation in Great Circle Navigation

2021 ◽  
Vol 9 (6) ◽  
pp. 603
Author(s):  
Mate Baric ◽  
David Brčić ◽  
Mate Kosor ◽  
Roko Jelic
Keyword(s):  
Trigonometric Function ◽  
Great Circle ◽  
Trigonometric Functions ◽  
Spherical Trigonometry ◽  
Software Packages ◽  
Vector Algebra ◽  
Computer Aided ◽  
Essential Knowledge

Based on traditional expressions and spherical trigonometry, at present, great circle navigation is undertaken using various navigational software packages. Recent research has mainly focused on vector algebra. These problems are calculated numerically and are thus suited to computer-aided great circle navigation. However, essential knowledge requires the navigator to be able to calculate navigation parameters without the use of aids. This requirement is met using spherical trigonometry functions and the Napier wheel. In addition, to facilitate calculation, certain axioms have been developed to determine a vessel’s true course. These axioms can lead to misleading results due to the limitations of the trigonometric functions, mathematical errors, and the type of great circle navigation. The aim of this paper is to determine a reliable trigonometric function for calculating a vessel’s course in regular and composite great circle navigation, which can be used with the proposed axioms. This was achieved using analysis of the trigonometric functions, and assessment of their impact on the vessel’s calculated course and established axioms.

scholarly journals Complex Acoustic Gravity Wave Behaviors to a Mathematical Model Arising in Nonlinear Mathematical Physics

2018 ◽  
Vol 22 ◽  
pp. 01032
Author(s):  
Tolga Akturk ◽  
Tukur Abdulkadir Sulaiman ◽  
Haci Mehmet Baskonus ◽  
Hasan Bulut
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Physical Interpretation ◽  
Physical Meaning ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Acoustic Gravity Wave ◽  
Mathematica Software

In this article, we utilize the powerful sine-Gordon expansion method (SGEM) in constructing some new solutions to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation by using the Mathematica software. We successfully obtain some new travelling solutions bearing some new structures such as trigonometric function, exponential function and hyperbolic function structures. We claim that some of our results are complex in structure. All the solutions obtained verified the the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. To illustrate our results, present the numerical simulation of all the obtained solutions in this study by selecting appropriate values of the parameters. Furthermore, we give the physical interpretation of all the graphics. We also give the physical meaning to some of the obtained results in this study.

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

2018 ◽  
Vol 32 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu ◽  
Elif Nuray
Keyword(s):  
Numerical Simulation ◽  
Solitary Wave ◽  
Riccati Equation ◽  
Physical Meaning ◽  
Trigonometric Function ◽  
Solitary Wave Solutions ◽  
Integration Schemes ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

scholarly journals Application of Pontryagin’s Minimum Principle in Optimum Time of Missile Manoeuvring

CAUCHY ◽  
2016 ◽  
Vol 4 (3) ◽  
pp. 107
Author(s):  
Sari Cahyaningtias ◽  
Subchan Subchan
Keyword(s):  
Numerical Simulation ◽  
Minimum Principle ◽  
Terminal Velocity ◽  
Initial Condition ◽  
Pontryagin’S Minimum Principle ◽  
Fixed Target ◽  
Optimum Time ◽  
Self Defense ◽  
Pontryagin's Minimum Principle ◽  
Aerial Vehicle

Missile is a guided weapon and designed to protect outermost island from a thread of other country. It, commonly, is used as self defense. This research presented surface-to-surface missile in final dive manoeuvre for fixed target. Furthermore, it was proposed manoeuvring based on unmanned aerial vehicle (UAV), autopilot system, which needs accuration and minimum both time and thrust of missile while attacking object. This paper introduced pontryagin’s Minimum Principle, which is useable to solve the problem. The numerical solution showed that trajectory of the missile is split it up in three sub-intervals; flight, climbing, and diving. The numerical simulation showed that the missile must climb in order to satisfy the final dive condition and the optimum time of a missile depend on initial condition of the altitude and the terminal velocity

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