Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics by Haileyesus Tessema Alemneh

“…From the analysis using center manifold theory, the model exhibits forward bifurcation. …”
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Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect by Xinhong Pan, Min Zhao, Chuanjun Dai, Yapei Wang

“…Second, the formulae that determine the direction of the Hopf bifurcation and the stability of periodic solutions are obtained using the normal form and the center manifold theory. Furthermore, our main results are illustrated using numerical simulations.…”
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Workplace surveillance: examining current instruments, limitations and legal background issues by Ulrike Hugl

“…Reasons for employers to monitor employees’ behavior are manifold: from an avoidance of malicious insider threats, the prevention of image damage, increased productivity, and through to reduced costs. …”
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On the structural stability of a simple cosmological model in R + αR2 theory of gravity by Orest Hrycyna

“…Using the invariant centre manifold, we demonstrate that, in the Einstein frame, there exists a zero-measure set of initial conditions that lead from an unstable to a stable de Sitter state. …”
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Étude des $(n+1)$-tissus de courbes en dimension $n$ by Dufour, Jean-Paul, Lehmann, Daniel

“…For $(n+1)$-webs by curves in an ambiant $n$-dimensional manifold, we first define a generalization of the well known Blaschke curvature of the dimension two, which vanishes iff the web has the maximum possible rank which is one. …”
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On the Existence of Polynomials with Chaotic Behaviour by Nilson C. Bernardes, Alfredo Peris

“…We also study distributional chaos for polynomials and show that every infinite-dimensional separable Banach space supports polynomials of arbitrary positive degree that have a dense distributionally scrambled linear manifold.…”
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Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost by S. S. Askar, Ahmed M. Alshamrani

“…One of those fixed points is Nash equilibrium, and the discussion shows that it can be unstable through flip and Neimark–Sacker bifurcation. The invariant manifold for the game’s map is analyzed. Furthermore, the case when both competing firms are independent is investigated. …”
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Dynamical Analysis of a Computer Virus Model with Delays by Juan Liu, Carlo Bianca, Luca Guerrini

“…Moreover the direction of the Hopf bifurcation and stability of the bifurcating period solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical investigations are carried out to show the feasibility of the theoretical results.…”
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Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model by Xueli Chen, Lishun Ren

“…The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. …”
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Three-Dimensional Pseudomanifolds on Eight Vertices by Basudeb Datta, Nandini Nilakantan

“…So, a normal 2-pseudomanifold triangulates a connected closed 2-manifold. But, normal d-pseudomanifolds form a broader class than triangulations of connected closed d-manifolds for d≥3. …”
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Novel DOA estimation method for coherent wideband LFM signals by Peng,LIUKai-hua LUO, Jie-xiao YU, Yong-tao MA

“…A novel direction of arrival (DOA) estimation method for coherent wideband linear frequency modulation (LFM) signals was proposed.Based on the dechirping property of LFM signal in fractional Fourier domain,a new array data model was constructed,then the matrix reconstruction and MUSIC algorithm were used to estimate the DOA of coherent LFM signals.If there were multiple groups of coherent LFM signals incident,separated them in different energy-concentrated domains first,then carried the DOA estimation on each of the groups.Owing to fully excavating the time-frequency information included in observed signals,this method has good resolution ability and anti-noise performance,and the number of DOA that can be resolved is also increased.In addition,this method has no array redundancy and aperture loss,and can be applied to arbitrary array manifold.Simulation results show that this method can obtain nearly 8dB signal-to-noise ratio gain compared with the conventional method.…”
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Stability and Hopf Bifurcation Analysis for a Stage-Structured Predator-Prey Model with Discrete and Distributed Delays by Ruiqing Shi, Junmei Qi, Sanyi Tang

“…Secondly, by use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. …”
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Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber by Fatemeh Helen Ghane, Mahboubeh Nazari, Mohsen Saleh, Zahra Shabani

“…We consider step and soft skew products over the Bernoulli shift which have an -dimensional closed manifold as a fiber. It is assumed that the fiber maps Hölder continuously depend on a point in the base. …”
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Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays by Xue Zhang, Qing-ling Zhang, Zhongyi Xiang

“…In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold argument. Finally, numerical simulations are included supporting the theoretical analysis and displaying the complex dynamical behavior of the model outside the domain of stability.…”
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Seven-dimensional considerations of Einstein's connection. I. The recurrence relations of the first kind in n-g-UFT by Mi Ae Kim, Keum Sook So, Chung Hyun Cho, Kyung Tae Chung

“…Einstein's connection in a generalized Riemannian manifold Xn has been investigated by many authors for lower-dimensional cases n=2,…,6. …”
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Regularization of the Boundary-Saddle-Node Bifurcation by Xia Liu

“…Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.…”
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Pseudoinversion of degenerate metrics by C. Atindogbe, J.-P. Ezin, Joël Tossa

“…Let (M,g) be a smooth manifold M endowed with a metric g. A large class of differential operators in differential geometry is intrinsically defined by means of the dual metric g∗ on the dual bundle TM∗ of 1-forms on M. …”
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Adaptive Control for Singularly Perturbed Systems by Kameron Eves, John Valasek

“…This causes complex interactions between the fast state reference model and the manifold to which the fast states converge. It is proven that under certain conditions the system still converges to the reference model despite these complex interactions. …”
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Can Libya survive as a single State? by George Joffé

“…Ever since the Qadhafi regime collapsed in late October 2011, the survival of the Libyan state has been opened to increasing question. The causes are manifold; the collapse of the Libyan army in the wake of the NATO-led attacks, the hostility of Britain and France, the roles played by the Gulf states, Turkey and Egypt, and the growth of extremism against the background of the privatised violence of the militias have all contributed towards its impending collapse. …”
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Robust Adaptive Fractional Fast Terminal Sliding Mode Controller for Microgyroscope by Juntao Fei, Zhe Wang, Xiao Liang

“…A new fast terminal switching manifold is defined to ensure fast finite convergence of the system states, where a fractional-order differentiation term emerges into terminal sliding surface, which additionally generates an extra degree of freedom and leads to better performance. …”
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