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Chaos synchronization is a procedure where one chaotic oscillator is forced to adjust the properties of another chaotic oscillator for all future states. This research paper studies and investigates the global chaos synchronization problem of two identical chaotic systems and two non-identical chaotic systems using the linear active control technique. Based on the Lyapunov stability theory and using the linear active control technique, the stabilizing controllers are designed for asymptotically global stability of the closed-loop system for both identical and non-identical synchronization. Numerical simulations and graphs are imparted to justify the efficiency and effectiveness of the proposed scheme. All simulations have been done by using mathematica 9. © 2014 Wiley Periodicals, Inc. Complexity 21: 379-386, 2015 [ABSTRACT FROM AUTHOR]

This paper addresses the chaos control and synchronization problems of a hyperchaotic system. It is assumed that the parameters of the hyperchaotic system are unknown and the system is perturbed by the external disturbance. Based on the Lyapunov stability theory and the adaptive control theory, suitable nonlinear controllers are designed for the asymptotic stability of the closed-loop system both for stabilization of hyperchaos at the origin and complete synchronization of two identical hyperchaotic systems. Accordingly, suitable update laws are proposed to estimate the fully uncertain parameters. All simulation results are carried out to validate the effectiveness of the theoretical findings. The effect of external disturbance is under our discussion. [ABSTRACT FROM AUTHOR]

The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9. [ABSTRACT FROM AUTHOR]

This study aimed to explore the influences of overcrowded classroom on the academic achievement of students at secondary school level in Khyber Pakhtunkhwa. Objective of the study was to explore the effect of overcrowded classroom on the academic achievement of students. Mixed method approach was applied for this research study. Sample of the study consisted of 600 10th grade students, 143 secondary school teachers and 30 principals selected through multistage cluster and simple random sampling technique. Quantitative data collected for the last five years result(2013-17) of 10th grade students from the Gazette book and also through self-developed questionnaires. Items of the questionnaire were developed on the basis of the problems of overcrowded classrooms with five point's Likert type rating scale. Qualitative data collected from the principals through interview. The results showed that there was a very weak correlation between the 10th grade students enrolled and their pass percentage in the SSC(A) exams for the years 2013-17. The study showed that there was much agreement between the views of teachers, students and principals on the issue. It was concluded from the current study that an overcrowded classroom can influences the student's academic achievement. The study confirmed that all the sampled secondary schools were lacking enough classrooms, teaching staffs and mostly the classrooms were overcrowded. It was recommended that class size may be of 35 students, shortage of teaching staffs and additional classrooms may be constructed to overcome the problem of overcrowded classroom. [ABSTRACT FROM AUTHOR]