The Experts below are selected from a list of 4089 Experts worldwide ranked by ideXlab platform
Yi Wang - One of the best experts on this subject based on the ideXlab platform.
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prevalent behavior of smooth Strongly Monotone discrete time dynamical systems
arXiv: Dynamical Systems, 2021Co-Authors: Yi Wang, Jinxiang Yao, Yufeng ZhangAbstract:For C1-smooth Strongly Monotone discrete-time dynamical systems, it is shown that ``convergence to linearly stable cycles" is a prevalent asymptotic behavior in the measuretheoretic sense. The results are then applied to classes of time-periodic parabolic equations and give new results on prevalence of convergence to periodic solutions. In particular, for equations with Neumann boundary conditions on convex domains, we show the prevalence of the set of initial conditions corresponding to the solutions that converge to spatiallyhomogeneous periodic solutions. While, for equations on radially symmetric domains, we obtain the prevalence of the set of initial values corresponding to solutions that are asymptotic to radially symmetric periodic solutions.
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Almost automorphy of minimal sets for $C^1$-smooth Strongly Monotone skew-product semiflows on Banach spaces
arXiv: Dynamical Systems, 2021Co-Authors: Yi Wang, Jinxiang YaoAbstract:We focus on the presence of almost automorphy in Strongly Monotone skew-product semiflows on Banach spaces. Under the $C^1$-smoothness assumption, it is shown that any linearly stable minimal set must be almost automorphic. This extends the celebrated result of Shen and Yi [Mem. Amer. Math. Soc. 136(1998), No. 647] for the classical $C^{1,\alpha}$-smooth systems. Based on this, one can reduce the regularity of the almost periodically forced differential equations and obtain the almost automorphic phenomena in a wider range.
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dynamics alternatives and generic convergence for c1 smooth Strongly Monotone discrete dynamical systems
Journal of Differential Equations, 2020Co-Authors: Yi Wang, Jinxiang YaoAbstract:Abstract For C 1 -smooth Strongly Monotone discrete-time dynamical systems, we prove dynamics alternatives, which concludes that any compact orbit is either asymptotic to a linearly stable cycle; or manifestly unstable. For this purpose we improve several properties of the exponential separation for continuous maps. The generic convergence to cycles is obtained as a by-product of the dynamics alternatives.
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Generical behavior of flows Strongly Monotone with respect to high-rank cones
2019Co-Authors: Feng Lirui, Yi Wang, Wu JianhongAbstract:We consider a $C^{1,\alpha}$ smooth flow in $\mathbb{R}^n$ which is "Strongly Monotone" with respect to a cone $C$ of rank $k$, a closed set that contains a linear subspace of dimension $k$ and no linear subspaces of higher dimension. We prove that orbits with initial data from an open and dense subset of the phase space are either pseudo-ordered or convergent to equilibria. This covers the celebrated Hirsch's Generic Convergence Theorem in the case $k=1$, yields a generic Poincar\'{e}-Bendixson Theorem for the case $k=2$, and holds true with arbitrary dimension $k$. Our approach involves the ergodic argument using the $k$-exponential separation and the associated $k$-Lyapunov exponent (that reduces to the first Lyapunov exponent if $k=1$)
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Phase-translation group actions on Strongly Monotone skew-product semiflows
Transactions of the American Mathematical Society, 2012Co-Authors: Yi WangAbstract:We establish a convergence property for pseudo-bounded forward orbits of Strongly Monotone skew-product semiflows with invariant phasetranslation group actions. The results are then applied to obtain global convergence of certain chemical reaction networks whose associated systems in reaction coordinates are Monotone, as well as the dynamics of certain reactiondiffusion systems in time-recurrent structure including periodicity, almost periodicity and almost automorphy.
Charles E. Chidume - One of the best experts on this subject based on the ideXlab platform.
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New algorithms for approximating zeros of inverse Strongly Monotone maps and J-fixed points
Fixed Point Theory and Applications, 2020Co-Authors: Charles E. Chidume, Chinedu G. EzeaAbstract:Let E be a real Banach space with dual space $E^{*}$. A new class of relatively weakJ-nonexpansive maps, $T:E\rightarrow E^{*}$, is introduced and studied. An algorithm to approximate a common element of J-fixed points for a countable family of relatively weak J-nonexpansive maps and zeros of a countable family of inverse Strongly Monotone maps in a 2-uniformly convex and uniformly smooth real Banach space is constructed. Furthermore, assuming existence, the sequence of the algorithm is proved to converge Strongly. Finally, a numerical example is given to illustrate the convergence of the sequence generated by the algorithm.
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a strong convergence theorem for generalized φ Strongly Monotone maps with applications
Fixed Point Theory and Applications, 2019Co-Authors: Charles E. Chidume, Monday Ogudu Nnakwe, A AdamuAbstract:Let X be a uniformly convex and uniformly smooth real Banach space with dual space $X^{*}$ . In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-Strongly Monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-Strongly Monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.
Mathew O Aibinu - One of the best experts on this subject based on the ideXlab platform.
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On generalized $Phi$-Strongly Monotone mappings and algorithms for the solution of equations of Hammerstein type
International Journal of Nonlinear Analysis and Applications, 2021Co-Authors: Mathew O Aibinu, O T MewomoAbstract:In this paper, we consider the class of generalized $Phi$-Strongly Monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein type. The auxiliary mapping is the composition of bounded generalized $Phi$-Strongly Monotone mappings which satisfy the range condition. Suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized $Phi$-Strongly which satisfies the range condition. A sequence is constructed and it is shown that it converges Strongly to a solution of equations of Hammerstein type. The results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of Hammerstein type.
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Strong convergence theorems for Strongly Monotone mappings in Banach spaces
Boletim da Sociedade Paranaense de Matemática, 2021Co-Authors: Mathew O Aibinu, O T MewomoAbstract:Let $E$ be a uniformly smooth and uniformly convex real Banach space and $E^*$ be its dual space. Suppose $A : E\rightarrow E^*$ is bounded, Strongly Monotone and satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions and use the new geometric properties of Banach spaces to show the strong convergence of an iterative algorithm to the solution of $Ax=0$.
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algorithm for solutions of nonlinear equations of Strongly Monotone type and applications to convex minimization and variational inequality problems
arXiv: Functional Analysis, 2020Co-Authors: Mathew O Aibinu, Surendra Thakur, Sibusiso MoyoAbstract:Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of (p, {\eta})-Strongly Monotone type, where {\eta} > 0, p > 1. An example is presented for the nonlinear equations of (p, {\eta})-Strongly Monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.
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Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems
Abstract and Applied Analysis, 2020Co-Authors: Mathew O Aibinu, Surendra Thakur, Sibusiso MoyoAbstract:Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of - Strongly Monotone type, where . An example is presented for the nonlinear equations of - Strongly Monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.
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algorithm for the generalized φ Strongly Monotone mappings and application to the generalized convex optimization problem
Proyecciones (antofagasta), 2019Co-Authors: Mathew O Aibinu, O T MewomoAbstract:Let E be a uniformly smooth and uniformly convex real Banach space and E∗ be its dual space. We consider a multivalued mapping A : E → 2E∗ which is bounded, generalized Φ-Strongly Monotone and such that for all t > 0, the range R(Jp+tA) = E∗, where Jp (p > 1) is the generalized duality mapping from E into 2E∗ . Suppose A−1(0) = ∅, we construct an algorithm which converges Strongly to the solution of 0 ∈ Ax. The result is then applied to the generalized convex optimization problem.
A Adamu - One of the best experts on this subject based on the ideXlab platform.
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a strong convergence theorem for generalized φ Strongly Monotone maps with applications
Fixed Point Theory and Applications, 2019Co-Authors: Charles E. Chidume, Monday Ogudu Nnakwe, A AdamuAbstract:Let X be a uniformly convex and uniformly smooth real Banach space with dual space $X^{*}$ . In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-Strongly Monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-Strongly Monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.
Eduardo D Sontag - One of the best experts on this subject based on the ideXlab platform.
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a remark on singular perturbations of Strongly Monotone systems
Conference on Decision and Control, 2006Co-Authors: Liming Wang, Eduardo D SontagAbstract:This paper extends to singular perturbations of Strongly Monotone systems a result of Hirsch's on generic convergence to equilibria.
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Almost Global Convergence in Singular Perturbations of Strongly Monotone Systems
arXiv: Dynamical Systems, 2006Co-Authors: Liming Wang, Eduardo D SontagAbstract:This paper deals with global convergence to equilibria, and in particular Hirsch's generic convergence theorem for Strongly Monotone systems, for singular perturbations of Monotone systems.
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A Global Convergence Result for Strongly Monotone Systems with Positive Translation Invariance
arXiv: Classical Analysis and ODEs, 2006Co-Authors: David Angeli, S. Marta, Eduardo D SontagAbstract:We show that Strongly Monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. An application to a reaction of interest in biochemistry is provided as an illustration.
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CDC - A Remark on Singular Perturbations of Strongly Monotone Systems
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Liming Wang, Eduardo D SontagAbstract:This paper extends to singular perturbations of Strongly Monotone systems a result of Hirsch's on generic convergence to equilibria.
