Quaternionic-valued ordinary differential equations. The Riccati equation
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Publication:1032872
DOI10.1016/j.jde.2009.06.015zbMath1191.34054OpenAlexW2089251565MaRDI QIDQ1032872
Publication date: 5 November 2009
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2009.06.015
Periodic solutions to ordinary differential equations (34C25) Growth and boundedness of solutions to ordinary differential equations (34C11) Applications of operator theory to differential and integral equations (47N20) Asymptotic properties of solutions to ordinary differential equations (34D05)
Related Items (31)
Geometry of Riccati equations over normed division algebras ⋮ Solving quaternion ordinary differential equations with two-sided coefficients ⋮ General theory of the higher-order linear quaternion q-difference equations through the quaternion determinant algorithm and the characteristic polynomial ⋮ Investigation of controllability and observability for linear quaternion-valued systems from its complex-valued systems ⋮ Existence and global exponential stability of anti-periodic solutions for quaternion-valued cellular neural networks with time-varying delays ⋮ Polynomial differential equations over the quaternions ⋮ A decomposition method for solving quaternion differential equations ⋮ Fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays ⋮ Sampling expansions associated with quaternion difference equations ⋮ Boundary value problems of quaternion-valued differential equations: solvability and Green's function ⋮ Numerical solutions of quaternionic Riccati equations ⋮ Pseudo‐differential operator in quaternion space ⋮ Spherical essentially non-oscillatory (SENO) interpolation ⋮ The existence and stability of two periodic solutions on a class of Riccati's equation ⋮ A UNIFIED ANALYSIS OF LINEAR QUATERNION DYNAMIC EQUATIONS ON TIME SCALES ⋮ Lie symmetries for Lie systems: applications to systems of ODEs and PDEs ⋮ General theory of the higher-order quaternion linear difference equations via the complex adjoint matrix and the quaternion characteristic polynomial ⋮ Global structure of quaternion polynomial differential equations ⋮ Low-dimensional dynamics in non-Abelian Kuramoto model on the 3-sphere ⋮ On the second Lyapunov method for quaternionic differential equations ⋮ Existence and uniqueness results for quaternion-valued nonlinear impulsive differential systems ⋮ One-dimensional quaternion homogeneous polynomial differential equations ⋮ Floquet theory for quaternion-valued differential equations ⋮ Quaternionic-valued ordinary differential equations. II: Coinciding sectors ⋮ A new quaternion hyper-complex space with hyper argument and basic functions via quaternion dynamic equations ⋮ Global solvability criteria for quaternionic Riccati equations ⋮ An algorithm for solving linear nonhomogeneous quaternion-valued differential equations and some open problems ⋮ Unnamed Item ⋮ Global behaviour of quaternion Riccati rational difference equation ⋮ Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem ⋮ Basic Theory of Impulsive Quaternion-Valued Linear Systems
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