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Forthcoming and Online First Articles
International Journal of Applied Nonlinear Science
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International Journal of Applied Nonlinear Science (5 papers in press)
Power series solution and conservation laws of fractional Whitham-Broer-Kaup equation by Hemanta Mandal, B. Bira Abstract: In this work, symmetry group of transformations for the system of time fractional Whitham-Broer-Kaup (WBK) equations are constructed. The transformations are used to reduce the given system of fractional partial differential equations (FPDEs) to fractional ordinary differential equations (FODEs). Further, the explicit power series solution of the given system of equations is obtained. Finally, The conservation laws of the governing system of equations is studied.rn Keywords: Lie symmetry; power series solution; fractional WBK equation; conservation laws.
Dislocated Dual HPS Between Integer & Complex Fractional Order Chaotic Systems Using Tracking Controllers With Application by Ayub Khan, Pushali Trikha, Taqseer Khan Abstract: In this article, the dislocated dual hybrid projective synchronization on two chaotic integer order master systems and two chaotic complex fractional order slave systems is realized.Suitable tracking controllers are designed based on the stability theory of the fractional differential equations.Numerical Simulations are performed on complex fractional order Lu system and complex fractional order Lorenz system as slave systems which verify the effectiveness of the tracking control strategy.Comparisons have been made with previously published literature. The application of the designed synchronization scheme has been applied in the area of secure communication. Keywords: Chaos Synchronization ; Tracking Control Method ; Dislocated Synchronization ; Dual Hybrid Projective Synchronization ; Secure Communication.
A bistable memristor-based circuit system and its implementation by Chen Zhen, Li Chun Lai, Qian Kun Abstract: This paper introduces a fourth-order oscillation circuit by replacing Chua's diode with a voltage controlled memristor and removing the resistor of canonical Chuas circuit. The system equations are built based on the circuit theory, the dissipation of the system and the stability of the equilibrium point are analyzed. Dynamic behaviors of the system have been studied by using phase portraits, bifurcation diagrams and Lyapunov spectrums. The analysis results show that the proposed system has bistability phenomenon of chaotic or periodic states and possesses complex transient dynamics under different parameter and initial conditions. This kind of bistability pattern reflects the sensitivity of system dynamics to initial condition, thus it can be used to generate random number and encrypt data information, and can also be used to realize bistable switch in the field of storage and computing. An analog electronic circuit is then designed to verify the numerical simulation results. Keywords: Chua's circuit; Memristor; Dynamic behavior; Bistability.
Modified Taylor wavelets approach to the numerical results of second order differential equatio by Ankit Kumar, Sag Ram Verma Abstract: In this paper, we present a new method which is based on the derivative operational matrix of modified Taylor wavelets (DOMMTWs) with collocation points for approximate solutions of a class of differential equations of second order. The idea behind using the DOMMTWs method is to converts the introduce problems into the equivalent set of algebraic equations. To the obtained results for some given problems are guaranteed that, the introduced method provides the best approximate solution to a class of second order differential equations. Keywords: Wavelet; Taylor wavelets; Modified Taylor wavelets; Collocation points; second order differential equations; Derivative operational matrix.
Emergence of complex dynamic behaviors in the Chua's circuit with a nonlinear inductor by Paul Didier KAMDEM KUATE, Njimboh Henry Alombah, Hilaire Fotsin Abstract: By considering a nonlinear inductor in the Chua's circuit, the dynamics of the circuit can be appreciated in a more generalized way and some neglected aspects of the realities of electronics are taken into consideration. In this work, the cubic and polynomial current-dependent models of the inductor are used. A systematic study is done with the help of tools such as bifurcation diagrams, Lyapunov spectrum and frequency power spectrum. The rich dynamics of the system reveal some complex behaviors and phenomena. Especially antimonotonicity, metastable chaos, coexistence of non-symmetric periodic orbits and chaotic attractors, phenomena that were not observed in the classical and the canonical Chua's circuit. Keywords: Chua's circuit; Nonlinear inductor; Antimonotonicity; metastable chaos; Coexistence of attractors.