Related papers: Spatio-temporal canards in neural field equations
We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex spatio-temporal behavior emerges as the system…
The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…
We present a study on the emergence of a variety of spatio temporal patterns among neurons that are connected in a multiplex framework, with neurons on two layers with different functional couplings. With the Hindmarsh-Rose model for the…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
Much of the information the brain processes and stores is temporal in nature - a spoken word or a handwritten signature, for example, is defined by how it unfolds in time. However, it remains unclear how neural circuits encode complex…
We investigate singular geometries which can be associated with warped branes in arbitrary dimensions. If the brane tension is allowed to be variable, the extremum condition for the action requires additional constraints beyond the solution…
Hippocampal place and time cells encode spatial and temporal aspects of experience. Both have the same neural substrate, but have been modeled as having different functions and mechanistic origins, place cells as continuous attractors, and…
Scaffolding proteins that direct the assembly of multiple kinases into a spatially localized signaling complex are often essential for the maintenance of an appropriate biological response. Although scaffolds are widely believed to have…
Executing complex manipulation in cluttered environments requires satisfying coupled geometric and temporal constraints. Although Spatio-Temporal Logic (SpaTiaL) offers a principled specification framework, its use in gradient-based…
Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with…
In recent years, there has been increasing interest in developing models and tools to address the complex patterns of connectivity found in brain tissue. Specifically, this is due to a need to understand how emergent properties emerge from…
We develop a functional-analytical machinery for studying the quadratic regulator problem arising from spectra perturbations of infinite-dimensional dynamical systems. In particular, we are interested in applications to inertial manifolds…
Nonlinear Schr\"odinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schr\"odinger equation describes coherent states. Such modes are…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
We consider double canard cycles including two canards in singularly perturbed planar systems with two canard points. Previous work studied the complex oscillations including relaxation oscillations and canard cycles in singularly perturbed…
Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between…
A characteristic matrix function captures the spectral information of a bounded linear operator in a matrix-valued function. In this article, we consider a delay differential equation with one discrete time delay and assume this equation is…
Understanding the dynamics of large-scale brain models remains a central challenge due to the inherent complexity of these systems. In this work, we explore the emergence of complex spatiotemporal patterns in a large scale-brain model…