Functional iteration for solving nonlinear system equations

The aim of this work is to present the numerical results of the influenza disease nonlinear system using the feed forward artificial neural networks (ANNs) along with the optimization of the combination of global and local search schemes. The genetic algorithm (GA) and active-set method (ASM), i.e., GA-ASM, are implemented as global and local search schemes. The mathematical nonlinear influenza disease system is dependent of four classes, susceptible S(u), infected I(u), recovered R(u) and cross-immune individuals C(u). For the solutions of these classes based on influenza disease system, the design of an objective function is presented using these differential system equations and its corresponding initial conditions. The optimization of this objective function is using the hybrid computing combination of GA-ASM for solving all classes of the influenza disease nonlinear system. The obtained numerical results will be compared by the Adams numerical results to check the authenticity of the designed ANN-GA-ASM. In addition, the designed approach through statistical based operators shows the consistency and stability for solving the influenza disease nonlinear system.

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Effect of System Noise on Chaotic Behavior in Roessler Type Nonlinear System

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127497001953 ◽

1997 ◽

Vol 07 (12) ◽

pp. 2871-2879 ◽

Cited By ~ 3

Author(s):

S. Ogata ◽

T. Iwayama ◽

S. Terachi

Keyword(s):

Nonlinear System ◽

Chaotic Behavior ◽

Random Noise ◽

Transformation Method ◽

Point Of View ◽

Controlling Chaos ◽

System Parameters ◽

System Noise ◽

System Equations ◽

Dc Bias

The present paper describes the effects of the system noise on the chaotic behavior of the Roessler type signal from the point of view of controlling chaos. We have investigated the system equations by a variable transformation method and have then carried out computer simulations to verify our theoretical consideration for a DC bias as system noise. These approaches reveal that the DC bias brings about the direct effect on the system parameters in the equations, while the random noise hardly affects the chaotic system.

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Stiffness synthesis of 3-DOF planar 3RPR parallel mechanisms

Robotica ◽

10.1017/s0263574715000363 ◽

2015 ◽

Vol 34 (12) ◽

pp. 2776-2787 ◽

Cited By ~ 1

Author(s):

Kefei Wen ◽

Chan-Bae Shin ◽

Tae Won Seo ◽

Jeh Won Lee

Keyword(s):

Nonlinear System ◽

Parallel Mechanisms ◽

End Effector ◽

Stiffness Analysis ◽

Pure Rotation ◽

Arbitrary Configuration ◽

Synthesis Strategy ◽

System Equations ◽

Three Degree Of Freedom ◽

Reference Input

SUMMARYForce control is important in robotics research for safe operation in the interaction between a manipulator and a human operator. The elasticity center is a very important characteristic for controlling the force of a manipulator, because a force acting at the elasticity center results in a pure displacement of the end-effector in the same direction as the force. Similarly, a torque acting at the elasticity center results in a pure rotation of the end-effector in the same direction as the torque. A stiffness synthesis strategy is proposed for a desired elasticity center for three-degree-of-freedom (DOF) planar parallel mechanisms (PPM) consisting of three revolute-prismatic-revolute (3RPR) links. Based on stiffness analysis, the elasticity center is derived to have a diagonal stiffness matrix in an arbitrary configuration. The stiffness synthesis is defined to determine the configuration when the elasticity center and the diagonal matrix are given. The seven nonlinear system equations are solved based on one reference input. The existence and the solvability of the nonlinear system equations were analyzed using reduced Gröbner bases. A numerical example is presented to validate the method.

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Finding nonlinear system equations and complex network structures from data: A sparse optimization approach

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/5.0062042 ◽

2021 ◽

Vol 31 (8) ◽

pp. 082101 ◽

Cited By ~ 1

Author(s):

Ying-Cheng Lai

Keyword(s):

Nonlinear System ◽

Complex Network ◽

Sparse Optimization ◽

Optimization Approach ◽

Network Structures ◽

System Equations

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Model reduction of the tippedisk: a path to the full analysis

Nonlinear Dynamics ◽

10.1007/s11071-021-06649-z ◽

2021 ◽

Author(s):

Simon Sailer ◽

Remco I. Leine

Keyword(s):

Stability Analysis ◽

Nonlinear System ◽

Full Detail ◽

Qualitative Behavior ◽

Nonlinear Stability Analysis ◽

Full System ◽

Reduced Equations ◽

Highly Nonlinear ◽

System Equations ◽

Inversion Phenomenon

AbstractThe tippedisk is a mechanical-mathematical archetype for friction-induced instability phenomena that exhibits an interesting inversion phenomenon when spun rapidly. The inversion phenomenon of the tippedisk can be modeled by a rigid eccentric disk in permanent contact with a flat support, and the dynamics of the system can therefore be formulated as a set of ordinary differential equations. The qualitative behavior of the nonlinear system can be analyzed, leading to slow–fast dynamics. Since even a freely rotating rigid body with six degrees of freedom already leads to highly nonlinear system equations, a general analysis for the full system equations is not feasible. In a first step the full system equations are linearized around the inverted spinning solution with the aim to obtain a local stability analysis. However, it turns out that the linear dynamics of the full system cannot properly describe the qualitative behavior of the tippedisk. Therefore, we simplify the equations of motion of the tippedisk in such a way that the qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear stability analysis. The reduced equations are presented here in full detail and are compared numerically with the full model. Furthermore, using the reduced equations we give approximate closed form results for the critical spinning speed of the tippedisk.

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