Experimental data are often very complex since the underlying dynamical system may be unknown and the data may heavily be corrupted by noise. It is a crucial task to properly analyze data to get maximal information of the underlying dynamical system. This paper presents a novel principal component analysis PCA method based on symplectic geometry, called symplectic PCA SPCA , to study nonlinear ...

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...