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In this paper, a symplectic algorithm is utilized to investigate constrained Hamiltonian systems. However, the symplectic method cannot be applied directly to the constrained Hamiltonian equations due to the non-canonicity. We firstly discuss the canonicalization method of the constrained Hamiltonian systems. The symplectic method is used to constrain Hamiltonian systems on the basis of the canonicalization, and then the numerical simulation of the system is carried out. An example is presented to illustrate the application of the results. By using the symplectic method of constrained Hamiltonian systems, one can solve the singular dynamic problems of nonconservative constrained mechanical systems, nonholonomic constrained mechanical systems as well as physical problems in quantum dynamics, and also available in many electromechanical coupled systems. [ABSTRACT FROM AUTHOR]

In this paper, a fractional order economic system is studied. An active control technique is applied to control chaos in this system. The stabilization of equilibria is obtained by both theoretical analysis and the simulation result. The numerical simulations, via the improved Adams-Bashforth algorithm, show the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

The ever-growing mobile station (MS) localization technologies provide an increasingly important role in all aspects of the wireless cellular systems and Internet of Things (IoT). The accurate MS location information is the basis in connection of different devices in IoT. The MS localization techniques based on time of arrival (TOA) trilateration algorithm, which determines the location of MS using an intersection point of three circles based on distances between MS and base stations (BS) and coordinates of BSs, have been actively studied. In general, the distance between the MS and BS is calculated by counting the number of delay samples or measuring the power of the received signal. Since the estimated distance (radius of a circle) between MS and BS is commonly increased, three circles may not meet at a single point, resulting in the estimation error of MS localization. In order to improve this problem, in this paper, we propose the hybrid TOA trilateration algorithm based on the line intersection algorithm for the general case for intersection of three circles and the comparison approach of intersection distances for the specific case where a small circle is located inside the area of two large circles. The line intersection algorithm has an excellent location estimation performance in the general case, but it does not work in the specific case. The comparison approach of intersection distances has good performance only for the specific case. In addition, we propose the mode selection algorithm to efficiently select a proper mode between the general and specific cases. The representative computer simulation examples are provided to verify the localization performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]