Yuri A. Kuznetsov

Bio: Yuri A. Kuznetsov is an academic researcher from Utrecht University. The author has contributed to research in topics: Homoclinic orbit & Homoclinic bifurcation. The author has an hindex of 26, co-authored 94 publications receiving 7811 citations. Previous affiliations of Yuri A. Kuznetsov include Centrum Wiskunde & Informatica & University of Houston.

Elements of applied bifurcation theory

Abstract: Introduction to Dynamical Systems * Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems * One-Parameter Bifurcations of Equilibria in Continuous-Time Systems * One-Parameter Bifurcations of Fixed Points in Discrete-Time Systems * Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Systems * Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria * Other One-Parameter Bifurcations in Continuous-Time Systems * Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems * Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems * Numerical Analysis of Bifurcations * A: Basic Notions from Algebra, Analysis, and Geometry * References * Index.

One-Parameter Bifurcations in Planar Filippov Systems

Abstract: We give an overview of all codim 1 bifurcations in generic planar discontinuous piecewise smooth autonomous systems, here called Filippov systems. Bifurcations are defined using the classical approach of topological equivalence. This allows the development of a simple geometric criterion for classifying sliding bifurcations, i.e. bifurcations in which some sliding on the discontinuity boundary is critically involved. The full catalog of local and global bifurcations is given, together with explicit topological normal forms for the local ones. Moreover, for each bifurcation, a defining system is proposed that can be used to numerically compute the corresponding bifurcation curve with standard continuation techniques. A problem of exploitation of a predator–prey community is analyzed with the proposed methods.

Catastrophic shifts in ecosystems.

Abstract: All ecosystems are exposed to gradual changes in climate, nutrient loading, habitat fragmentation or biotic exploitation. Nature is usually assumed to respond to gradual change in a smooth way. However, studies on lakes, coral reefs, oceans, forests and arid lands have shown that smooth change can be interrupted by sudden drastic switches to a contrasting state. Although diverse events can trigger such shifts, recent studies show that a loss of resilience usually paves the way for a switch to an alternative state. This suggests that strategies for sustainable management of such ecosystems should focus on maintaining resilience.

Dynamical Systems in Neuroscience

Abstract: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

Early-warning signals for critical transitions

Abstract: Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.

Resilience thinking: integrating resilience, adaptability and transformability

Abstract: Resilience thinking addresses the dynamics and development of complex social-ecological systems (SES). Three aspects are central: resilience, adaptability and transformability. These aspects interrelate across multiple scales. Resilience in this context is the capacity of a SES to continually change and adapt yet remain within critical thresholds. Adaptability is part of resilience. It represents the capacity to adjust responses to changing external drivers and internal processes and thereby allow for development along the current trajectory (stability domain). Transformability is the capacity to cross thresholds into new development trajectories. Transformational change at smaller scales enables resilience at larger scales. The capacity to transform at smaller scales draws on resilience from multiple scales, making use of crises as windows of opportunity for novelty and innovation, and recombining sources of experience and knowledge to navigate social-ecological transitions. Society must seriously consider ways to foster resilience of smaller more manageable SESs that contribute to Earth System resilience and to explore options for deliberate transformation of SESs that threaten Earth System resilience.