An Effective Synchronization Approach to Stability Analysis for Chaotic Generalized Lotka–Volterra Biological Models Using Active and Parameter Identification Methods (original) (raw)
2020
In this work, we study hybrid projective combination synchronization scheme among identical chaotic generalized Lotka-Volterra three species biological systems using active control design. We consider here generalized Lotka-Volterra system containing two predators and one prey population existing in nature. An active control design is investigated which is essentially based on Lyapunov stability theory. The considered technique derives the global asymptotic stability using hybrid projective combination synchronization technique. In addition, the presented simulation outcomes and graphical results illustrate the validation of our proposed scheme. Prominently, both the analytical and computational results agree excellently. Comparisons versus others strategies exhibiting our proposed technique in generalized Lotka-Volterra system achieved asymptotic stability in a lesser time
2017
Abstract: Using the active control technique with Lyapunov stability theory and Routh-Hurwirtz criteria, the control functions are designed to achieve projective synchronization between two identical φ Van der Pol Oscillator (φ VDPOs) and two identical φ Duffing Oscillator (φ DOs), comprising φ VDPO and φ DO for the triple well configuration of the φ potential. The coefficient matrix of the error dynamics between each pair of projective synchronized systems is chosen such that the number of active control functions reduces from two to one, thereby, significantly reducing controller complexity in the design. The designed controllers enable the state variables of the response system to achieve projective synchronization with those of the drive system. Also, the coupling parameter that leads to the fastest synchronization time was determined. The results are validated using numerical simulations.
International Journal of Electrical and Computer Engineering (IJECE), 2017
The synchronization problem of chaotic systems using active modified projective non-linear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views. 1. INTRODUCTION Master-slave synchronization of chaotic systems is strikely nonlinear, since the aperiodic and nonreg-ular behavior of chaotic systems and their sensitivity to the initial conditions. Chaotic behavior may appear in many physical systems. So, chaos synchronization subject has received a great deal of attention in the last to decades, due to its potential applications in physics, chemistry, electrical engineering, secure communication and so on[1]. Up to now, many types of controling methods are revealed and investigated for control and synchronization of chaotic systems. Active method[2, 3, 4, 5, 6], adaptive method [7, 8, 9], linear feedback method [10, 11], nonlinear feedback method [12, 14, 15], sliding mode method [16, 17, 18], impulsive method [19], phase method [20], generalized method [21], robust synchronization [13] and projective method [22, 23, 24] are some of the introduced methods by the researchers. Among these methods, synchronization with some types of projective methods are extensively investigated in the last decades, since the faster synchronization due to its synchronization scaling factors, which master and slave chaotic systems would be synchronized up to a proportional rate. Projective lag method [25], modified projective synchronization (MPS) [26, 27, 28], function projective synchronization (FPS)[29], modified function projective synchronization [30, 28], generalized function projective synchronization [31, 32] and modified projective lag synchronization[33, 34] are some generalized schemes of projective method, which utilize some type of scaling factors. When the parameters of a chaotic system are known beforehand, active related methods are preferably chosen than adaptive methods. Active synchronization problem of two chaotic systems with known parameters are vastly investigated by the researchers. For example, in [5, 3, 35], the active controlling method is studied for synchronization of two typical chaotic systems. And also, in [2], an active method for controling the behavior of a unified chaotic system is presented. Chaos synchronization of complex Chen and Lu chaotic systems are addressed in citeMahmoud, with designing an active control method. Furthermore, in [36] active