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In this paper, we investigate the almost-sure exponential asymptotic stability of the trivial solution of a parabolic stochastic partial differential equation (SPDE) driven by multiplicative noise near the deterministic Hopf bifurcation point. We show the existence and uniqueness of the invariant measure under appropriate assumptions, and approximate the exponential growth rate via asymptotic expansion, given that the strength of the noise is small. This approximate quantity can readily serve as a robust indicator of the change of almost-sure stability. We apply the results to a simplified stochastic Moore-Greitzer PDE model in detecting the stall instabilities of modern jet-engine under the impact of multiplicative noise. A better understanding of the instability margin will eventually optimize the jet-engine operating range and thus lead to lighter and more efficient jet-engine design. [ABSTRACT FROM AUTHOR]

This paper is dedicated to Jim Cushing on the occasion of his 80th birthday. It is inspired by his work on evolutionary theory. We investigate the global dynamics of discrete-time phenotypic evolutionary models, both autonomous and periodic. We developed the theory of mixed monotone maps and applied it to show that the positive equilibrium of the autonomous evolutionary Ricker model of single and multi-species is globally asymptotically stable. Then we extend this result to the corresponding evolutionary Ricker model with periodic parameters. [ABSTRACT FROM AUTHOR]

We study reservoir computing, a machine learning method, from the viewpoint of learning dynamics. We present numerical results of learning the dynamics of the logistic map, one of the typical examples of chaotic dynamical systems, using a 30-node reservoir and a three-node reservoir. When the learning is successful, an attractor that is smoothly conjugate to the logistic map to be learned is observed in the phase space of the reservoir. Inspired by this numerical result, we introduce a degenerate reservoir system and use it to mathematically confirm this observation. We also show that reservoir computing can learn information about dynamics not included in the training data, which we believe is a remarkable feature of reservoir computing compared to other machine learning methods. We discuss this feature in connection with the above observation that there is a smooth conjugacy between the attractor in the reservoir and the dynamics to be learned. [ABSTRACT FROM AUTHOR]

In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres make no transitions between classes of motion. This is an important ideal for enhancing confinement. First, we present a weak formulation, based on the longitudinal adiabatic invariant, generalising omnigenity. To demonstrate that isodrasticity is strictly more general than omnigenity, we construct weakly isodrastic mirror fields that are not omnigenous. Then we present a strong formulation that is exact for guiding-centre motion. We develop a first-order treatment of the strong version via a Melnikov function and show that it recovers the weak version. The theory provides quantification of deviations from isodrasticity that can be used as objective functions in optimal design. The theory is illustrated with some simple examples. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic recently caused a huge impact on India, not only in terms of health but also in terms of economy. Understanding the spatio-temporal patterns of the disease spread is crucial for controlling the outbreak. In this study, we apply the compatible window-wise dynamic mode decomposition (CwDMD) and dynamic mode decomposition (DMD) techniques to the COVID-19 data of India to model the spatial-temporal patterns of the epidemic. We preprocess the COVID-19 data into weekly time-series at the state-level and apply both the CwDMD and DMD methods to decompose the data into a set of spatial-temporal modes. We identify the key modes that capture the dominant features of the COVID-19 spread in India and analyze their phase, magnitude, and frequency relationships to extract the temporal and spatial patterns. By incorporating rank truncation in each window, we have achieved greater control over the system’s output, leading to better results. Our results reveal that the COVID-19 outbreak in India is driven by a complex interplay of regional, demographic, and environmental factors. We identify several key modes that capture the patterns of disease spread in different regions and over time, including seasonal fluctuations, demographic trends, and localized outbreaks. Overall, our study provides valuable insights into the patterns of the COVID-19 outbreak in India using both CwDMD and DMD methods. These findings can help public health organizations to develop more effective strategies for controlling the spread of the pandemic. The CwDMD and DMD methods can be applied to other countries to identify the unique drivers of the outbreak and develop effective control strategies.

The shadowing property relationship between a uniformly convergent mapping sequence (f n) n = 1 ∞ and its limit mapping f in non-autonomous systems is discussed. Some sufficient and necessary conditions are given for that (f n) n = 1 ∞ is limit shadowing property, d ̲ -shadowing property or pseudo-orbit shadowing property. In particular, a computer simulation of an example is given to illustrate the shadowing property of (f n) n = 1 ∞ . In addition, it is proved that the sensitivity of (f n) n = 1 ∞ is equivalent to the sensitivity of f under the shadowing system. [ABSTRACT FROM AUTHOR]

Motivated by recent studies on the notions of lineability and spaceability in the context of linear dynamics, we investigate the existence of infinite-dimensional closed subspaces of frequently hypercyclic vectors for frequently hypercyclic composition operators, known in the literature as Koopman operators and extensively used in many applications (like, for instance, the analysis of the dynamics of economic models formulated in terms of dynamical systems). All the results are obtained on $L^p$ spaces, $1 \leq p < \infty$, and in the dissipative setting with the extra hypothesis of bounded distortion. This allows us, as a consequence, to deduce analogous conclusions for fundamental mathematical objects: bilateral weighted backward shifts on $\ell^p$ spaces. [ABSTRACT FROM AUTHOR]

Social balance theory describes allowable and forbidden configurations of thetopologies of signed directed social appraisal networks. In this paper, wepropose two discrete-time dynamical systems that explain how an appraisalnetwork \textcolor{blue}{converges to} social balance from an initiallyunbalanced configuration. These two models are based on two differentsocio-psychological mechanisms respectively: the homophily mechanism and theinfluence mechanism. Our main theoretical contribution is a comprehensiveanalysis for both models in three steps. First, we establish the well-posednessand bounded evolution of the interpersonal appraisals. Second, we fullycharacterize the set of equilibrium points; for both models, each equilibriumnetwork is composed by an arbitrary number of complete subgraphs satisfyingstructural balance. Third, we establish the equivalence among three distinctproperties: non-vanishing appraisals, convergence to all-to-all appraisalnetworks, and finite-time achievement of social balance. In addition totheoretical analysis, Monte Carlo validations illustrates how the non-vanishingappraisal condition holds for generic initial conditions in both models.Moreover, numerical comparison between the two models indicate that thehomophily-based model might be a more universal explanation for the formationof social balance. Finally, adopting the homophily-based model, we presentnumerical results on the mediation and globalization of local conflicts, thecompetition for allies, and the asymptotic formation of a single versus twofactions.

We study the frame properties of the Gabor systems G (g ; α , β) : = { e 2 π i β m x g (x - α n) } m , n ∈ Z. In particular, we prove that for Herglotz windows g such systems always form a frame for L 2 (R) if α , β > 0 , α β ≤ 1 . For general rational windows g ∈ L 2 (R) we prove that G (g ; α , β) is a frame for L 2 (R) if 0 < α , β , α β < 1 , α β ∉ Q and g ^ (ξ) ≠ 0 , ξ > 0 , thus confirming Daubechies conjecture for this class of functions. We also discuss some related questions, in particular sampling in shift-invariant subspaces of L 2 (R) . [ABSTRACT FROM AUTHOR]

The aim of this work is to propose and study dynamics of two fractional-order SIQRA malware propagation models and their discretizations. Positivity, boundedness and asymptotic stability properties of the proposed fractional-order models are analyzed rigorously. It is worthy noting that the global and uniform asymptotic stability properties of the fractional-order models are investigated based on appropriate Lyapunov functions. As an important consequence, the global asymptotic stability properties of the original integer-order models are also established completely. In addition, the fractional forward Euler method is utilized to discretize the fractional-order models. By rigorously mathematical analyses, we obtain step size thresholds which guarantee that the positivity, boundedness and asymptotic stability properties of the fractional-order models are preserved correctly by the discrete models. Consequently, simple conditions for reliable approximations for the fractional-order models are determined. Finally, a set of numerical examples is performed to illustrate and support the theoretical findings. The results show that the numerical examples are consistent with the constructed theoretical assertions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a modification of the well-known logistic family using a family of fuzzy numbers. The dynamics of this modified logistic map is studied by computing its topological entropy with a given accuracy. This computation allows us to characterize when the dynamics of the modified family is chaotic. Besides, some attractors that appear in bifurcation diagrams are explained. Finally, we will show that the dynamics induced by the logistic family on the fuzzy numbers need not be complicated at all. [ABSTRACT FROM AUTHOR]

An understanding of traffic statics and dynamics is critical for developing effective and efficient control strategies for a signalized road network with turning movements, especially under oversaturated conditions. In this study, we first describe traffic dynamics in a signalized double-ring network with the link queue model, which is a space-continuous approximation of the network kinematic wave model, and rewrite it as a switched affine system, assuming a triangular traffic flow fundamental diagram. Then we define periodic density evolution orbits as stationary states in the network and introduce a Poincaré map in densities, whose fixed points correspond to stationary states. With short cycle lengths and identical green times and retaining ratios in both rings, we are able to derive the closed form of the Poincaré map, from which we can analytically solve stationary states and study their stability properties; it is found that a stationary state can be asymptotically stable, Lyapunov stable, or unstable. By defining the network flow-density relation in stationary states as the macroscopic fundamental diagram (MFD), we analytically derive an approximate closed-form formula for MFD with green ratios and retaining ratios as parameters. We confirm that in stationary states the network flow rate may not be uniquely defined, and the network can reach a gridlock state at relatively low densities. We also analyze the convergence patterns to asymptotically stable gridlock states with different retaining ratios and initial densities. With more general signal settings and retaining ratios, we develop a secant method to numerically solve the fixed points of the Poincaré maps and plot the corresponding MFDs. Furthermore, numerical simulations are used to study traffic statics in a homogeneous signalized grid network; simulation results reveal a high level of similarity in traffic patterns between the signalized double-ring and grid networks and validate analytical insights obtained from the former. This study provides a springboard for future analytical and numerical studies on traffic statics and dynamics in more general signalized road networks.

In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible–infected–removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people. [ABSTRACT FROM AUTHOR]

This paper proposes models of learning process in teams of individuals whocollectively execute a sequence of tasks and whose actions are determined byindividual skill levels and networks of interpersonal appraisals and influence.The closely-related proposed models have increasing complexity, starting with acentralized manager-based assignment and learning model, and finishing with asocial model of interpersonal appraisal, assignments, learning, and influences.We show how rational optimal behavior arises along the task sequence for eachmodel, and discuss conditions of suboptimality. Our models are grounded inreplicator dynamics from evolutionary games, influence networks frommathematical sociology, and transactive memory systems from organizationscience.

In this paper, an adaptive generalised function projective synchronisation scheme of fractional-order chaotic systems with different dimensions and orders and fully unknown parameters is presented. On the basis of the Lyapunov method of fractional-order systems, a stability theorem of the fractional-order system with non-identical orders is proven. Using the fractional-order controller and adaptive control theory, sufficient conditions for synchronisation and unknown parameters update rules are obtained. Theoretical analysis and numerical simulations are provided to verify the validity of the proposed scheme. Moreover, synchronisation results are applied to secure communication via modified chaotic masking (MCM) method. The unpredictability of the scaling function matrix and the use of fractional-order systems with different orders can increase the security of the cryptosystem. The security analysis shows that the introduced algorithm has large key space, high sensitivity to encryption keys, higher security and the acceptable encryption speed. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model of illicit drug use in a population is studied using dynamical system theory. The work is largely concerned with the analysis of asymptotic behaviour of solutions to a six-dimensional system of differential equations modeling the influence of illicit drug use in the population. The model is mathematically well-posed based on positivity and boundedness of solutions. A key threshold which measures the potential spread of the illicit drug use in the population is derived analytically. The model is shown to exhibit forward bifurcation property, implying the existence, uniqueness and local stability of an illicit drug-present equilibrium. Furthermore, the global asymptotic dynamics of the model around the illicit drug-free and drug-present equilibria are extensively investigated using appropriate Lyapunov functions. Numerical simulations are carried out to complement the obtained theoretical results, and to examine the effects of some parameters, such as influence rate, rehabilitation rates of drug users and relapse rate, on the dynamical spread of illicit drug use in the population. Measures to guide against the menace of the illicit drug use are suggested. [ABSTRACT FROM AUTHOR]

In this paper, a particular discrete-time nonlinear and time-invariant system represented as a vector difference equation is analyzed for its stability properties. The motivation for analyzing this particular system is that it models gated recurrent unit neural networks commonly used and well known in machine learning applications. From the technical perspective, the analyses exploit the systems similarities to a convex combination of discrete-time systems, where one of the systems is trivial, and thus, the overall properties are mostly dependent on the other one. Stability results are formulated for the nonlinear system and its linearization with respect to the systems, in general, multiple equilibria. To motivate and illustrate the potential of these results in applications, some particular results are derived for the gated recurrent unit neural network models and a connection between local stability analysis and learning is provided. [ABSTRACT FROM AUTHOR]

We propose an interdisciplinary framework for time series classification, forecasting, and anomaly detection by combining concepts from Koopman operator theory, machine learning, and linear systems and control theory. At the core of this framework is nonlinear dynamic generative modeling of time series using the Koopman operator which is an infinite-dimensional but linear operator. Rather than working with the underlying nonlinear model, we propose two simpler linear representations or model forms based on Koopman spectral properties. We show that these model forms are invariants of the generative model and can be readily identified directly from data using techniques for computing Koopman spectral properties without requiring the explicit knowledge of the generative model. We also introduce different notions of distances on the space of such model forms which is essential for model comparison/clustering. We employ the space of Koopman model forms equipped with distance in conjunction with classical machine learning techniques to develop a framework for automatic feature generation for time series classification. The forecasting/anomaly detection framework is based on using Koopman model forms along with classical linear systems and control approaches. We demonstrate the proposed framework for human activity classification, and for time series forecasting/anomaly detection in power grid application. [ABSTRACT FROM AUTHOR]

We construct a three-factor modification of the R. Solow model taking into account final consumption and limited resources. The dynamics of a population is determined by the Verhulst equation, and the final consumption depends on the population. According to the Russian Federal State Statistics Service, the model parameters for the Ryazan Region were identified. An analytical and numerical study of the behavior of solutions of the resulting dynamical system is performed. [ABSTRACT FROM AUTHOR]

We present a method for both cross-estimation and iterated time series prediction of spatio-temporal dynamics based on local modelling and dimension reduction techniques. Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio–Cherry–Fenton model, and the Kuramoto–Sivashinsky model. [ABSTRACT FROM AUTHOR]

The main aim of this paper is the study of dynamical properties of the Laplacian-type coupled map lattice induced by the logistic family on a periodic lattice depending on two parameters: the state parameter of the logistic map and the coupling constant. For this purpose, tools like maximal Lyapunov exponent, approximate entropy, and the 0–1 test for chaos are introduced and applied to numerical simulations performed using a supercomputer. [ABSTRACT FROM AUTHOR]

This paper deals with a new purely data-driven method, called the spatio-temporal Koopman decomposition, to approximate spatio-temporal data as a linear combination of (possibly growing or decaying exponentially) standing or traveling waves. The method combines (i) either standard singular value decomposition (SVD) or higher-order SVD and (ii) either standard dynamic mode decomposition (DMD) or an extension of this method by the authors, called higher-order DMD. In particular, for periodic or quasiperiodic attractors, the method gives the spatio-temporal pattern as a superposition of standing and/or traveling waves, which are identified in an efficient and robust way. Such superposition may give the whole pattern as a modulated, periodic or quasiperiodic, standing or traveling wave. The method is illustrated in some simple toy-model dynamics, and its performance is tested in the identification of standing and traveling waves in the Ginzburg-Landau equation and of azimuthal waves in a rotating spherical shell with thermal convection. [ABSTRACT FROM AUTHOR]

We investigate multistability and global bifurcations in the general standard map, a biparametric two-dimensional map. Departing from the conservative case of the map, we describe the evolution of periodic solutions and their basins of attraction as dissipation builds up, paying special attention on how the biparametric variation affects multistability. We examine general and specific phenomena and behavior for three distinct dynamical regimes, namely small, moderate, and large damping and different forcing amplitudes. Also, we report numerically the mechanism of global bifurcations associated to small chaotic attractors in the multistable system. Several global bifurcations are investigated as dissipation increases. Specifically, through the characterization of an interior, a merging and a boundary crisis, we study the crucial role played by fundamental hyperbolic invariant structures, such as unstable periodic orbits and their stable and unstable invariant manifolds, in the mechanisms by which the phase space is globally transformed. [ABSTRACT FROM AUTHOR]

This paper aims at the sustainable development of resource-based industry. First, one-dimensional discrete dynamic model is formulated by considering exploitation and protection of renewable resource simultaneously, and then it is extended to two-dimensional dynamic model by assuming that government carries on the dynamic management to the exploitation speed of resource. The conditions of the existence and local stability of positive equilibrium are derived. The threshold of output is given which ensures the resource is stabilized at a fixed value. The global analysis of both models is represented by determining the feasible domain of attractor. The stability of positive fixed point at flip bifurcation and Neimark-Sacker bifurcation is respectively investigated with center manifold theorem and normal form. We also verify the given conclusions by the method of numerical analysis. In the end, we argued that if the government implements the dynamic quota management for resource exploitation, not only can we maintain a certain stock of resources so that people can get more resources permanently but also we can ensure a higher and wider output to meet the development of the industry. [ABSTRACT FROM AUTHOR]

In this paper we give an introduction to the notion of a normally hyperbolic invariant manifold (NHIM) and its role in chemical reaction dynamics.We do this by considering simple examples for one-, two-, and three-degree-of-freedom systems where explicit calculations can be carried out for all of the relevant geometrical structures and their properties can be explicitly understood. We specifically emphasize the notion of a NHIM as a 'phase space concept'. In particular, we make the observation that the (phase space) NHIM plays the role of 'carrying' the (configuration space) properties of a saddle point of the potential energy surface into phase space. We also consider an explicit example of a 2-degree-of-freedom system where a 'global' dividing surface can be constructed using two index one saddles and one index two saddle. Such a dividing surface has arisen in several recent applications and, therefore, such a construction may be of wider interest. [ABSTRACT FROM AUTHOR]

Classic convolutional codes are defined as the convolution of a message and a transfer function over $$\mathbb {Z}$$ . In this paper, we study time-varying convolutional codes over a finite group G of the form $${\mathbb {Z}}/N{\mathbb {Z}} \rtimes {\mathbb {Z}}/M{\mathbb {Z}}$$ . The goal of this study is to design codes with cryptographic properties. To define a message u of length k over the group G, we choose a subset E of G that changes at each encoding, and we put $$u = \sum _i u_iE(i)$$ . These subsets E are generated chaotically by a dynamical system, walking from a starting point ( x, y) on a space paved by rectangles, each rectangle representing an element of G. So each iteration of the dynamical system gives an element of the group which is saved on the current E. The encoding is done by a convolution product with a fixed transfer function. We have found a criterion to check whether an element in the group algebra can be used as a transfer function. The decoding process is realized by syndrome decoding. We have computed the minimum distance for the group $$G=\mathbb {Z}/7\mathbb {Z} \rtimes \mathbb {Z}/3\mathbb {Z}$$ . We found that it is slightly smaller than those of the best linear block codes. Nevertheless, our codes induce a symmetric cryptosystem whose key is the starting point ( x, y) of the dynamical system. Consequently, these codes are a compromise between error correction and security. [ABSTRACT FROM AUTHOR]

We are interested in the phenomenology of the asymptotic dynamics of piecewise contracting maps. We consider a wide class of such maps and we give sufficient conditions to ensure some general basic properties, such as the periodicity, the total disconnectedness or the zero Lebesgue measure of the attractor. These conditions show in particular that a non-periodic attractor necessarily contains discontinuities of the map. Under this hypothesis, we obtain numerous examples of attractors, ranging from finite to connected and chaotic, contrasting with the (quasi-)periodic asymptotic behaviours observed so far. [ABSTRACT FROM AUTHOR]

Assume thatis a probability space andis a metric space. Given a product measurable function, we examine connections between the iterates(in the sense of K. Baron and M. Kuczma, Colloq. Math. 37 (1977), 263–269) ofand the Markov operatorwith adjointof the form. Moreover, some results concerning the existence and the uniqueness of solutionsof the equationwill be also presented. [ABSTRACT FROM AUTHOR]

Given measure spaces $${(\Omega_{1}, \mathcal{A}_{1}, \mu_{1}),...,(\Omega_{N}, \mathcal{A}_{N}, \mu_{N}),}$$ functions $${\varphi_{1}: \mathbb{R}^{m} \times \Omega_{1} \rightarrow \mathbb{R}^{m},...,\varphi_{N}: \mathbb{R}^{m} \times \Omega_{N} \rightarrow \mathbb{R}^{m}}$$ and $${g: \mathbb{R}^{m} \rightarrow \mathbb{R}}$$ , we present results on the existence of solutions $${f: \mathbb{R}^{m} \rightarrow \mathbb{R}}$$ of the inhomogeneous poly-scale refinement type equation of the form in some special classes of functions. The results are obtained by Banach fixed point theorem applied to a perturbed Markov operator connected with the considered inhomogeneous poly-scale refinement type equation. [ABSTRACT FROM AUTHOR]

We study a family of discrete dynamical processes introduced by Novikoff, Kleinberg, and Strogatz that we call flashcard games. We prove a number of results on the evolution of these games, and in particular, we settle a conjecture of NKS on the frequency with which a given card appears. We introduce a number of generalizations and variations that we believe are of interest, and we provide a large number of open questions and problems. [ABSTRACT FROM AUTHOR]

In a previous work, for parallel dynamical systems over digraphs corresponding to the simplest Boolean functions AND and OR, we proved that only fixed or eventually fixed points appear, as it occurs over undirected dependency graphs. Nevertheless, for general Boolean functions, it was shown that any period can appear, depending on the Boolean function that infers the global evolution operator of the system and on the structure of the dependency digraph. Motivated by these results, in this work, we analyse the orbit structure of parallel discrete dynamical systems over some special digraph classes. [ABSTRACT FROM PUBLISHER]

In this article, we provide a matrix method in order to compute orbits of parallel and sequential dynamical systems on Boolean functions. In this sense, we develop algorithms for systems defined over directed (and undirected) graphs when the evolution operator is a general minterm or maxterm and, likewise, when it is constituted by independent local Boolean functions, so providing a new tool for the study of orbits of these dynamical systems. [ABSTRACT FROM AUTHOR]

Most aquatic vertebrates swim by lateral flapping of their bodies and caudal fins. While much effort has been devoted to understanding the flapping kinematics and its influence on the swimming efficiency, little is known about the stability (or lack of) of periodic swimming. It is believed that stability limits maneuverability and body designs/flapping motions that are adapted for stable swimming are not suitable for high maneuverability and vice versa. In this paper, we consider a simplified model of a planar elliptic body undergoing prescribed periodic heaving and pitching in potential flow. We show that periodic locomotion can be achieved due to the resulting hydrodynamic forces, and its value depends on several parameters including the aspect ratio of the body, the amplitudes and phases of the prescribed flapping.We obtain closedform solutions for the locomotion and efficiency for small flapping amplitudes, and numerical results for finite flapping amplitudes. This efficiency analysis results in optimal parameter values that are in agreement with values reported for some carangiform fish. We then study the stability of the (finite amplitude flapping) periodic locomotion using Floquet theory. We find that stability depends nonlinearly on all parameters. Interesting trends of switching between stable and unstable motions emerge and evolve as we continuously vary the parameter values. This suggests that, for live organisms that control their flapping motion, maneuverability and stability need not be thought of as disjoint properties, rather the organism may manipulate its motion in favor of one or the other depending on the task at hand. [ABSTRACT FROM AUTHOR]