Catastrophe Theory and Its Applications
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Catastrophe Theory and Its Applications

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Description

Catastrophe Theory and Its ApplicationsThis first integrated treatment of the main ideas behind Ren Thom's theory of catastrophes aims to make them accessible to scientists wishing to apply the theory in their own fields of research. The mathematical basis of the theory is therefore explained with a minimum of technicalities, although some knowledge of the calculus of variables is assumed. Thom's now famous list of seven elementary catastrophes, broadly classifying various types of

This first integrated treatment of the main ideas behind Ren Thom's theory of catastrophes aims to make them accessible to scientists wishing to apply the theory in their own fields of research. The mathematical basis of the theory is therefore explained with a minimum of technicalities, although some knowledge of the calculus of variables is assumed.
Thom's now-famous list of seven elementary catastrophes, broadly classifying various types of discontinuous change, is elucidated, as are the reasons for its appearance. Nearly half the book concentrates on detailed applications of the theory, emphasizing its uses in the physical sciences where applications can be made quantitative and can be experimentally verified. The more controversial and speculative applications to areas in the social sciences are also mentioned, but not discussed in detail.
Over 200 illustrations help clarify the ideas and applications in this volume, which will be of interest to researchers and postgraduate students in such diverse disciplines as engineering, mathematics, physics, and biology. 1978 edition. Bibliography.



Binding Type: Paperback
Publisher: Dover Publications
Published: 02/29/2012
ISBN: 9780486692715
Pages: 512
Weight: 1.58lbs
Size: 9.12h x 6.46w x 0.94d
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SKU: 91774461368

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Shan
New York, US
★★★★★ 5
Dog toy is tough and durable
Color: Blue&Red Fish
It’s great for aggressive chewers, my pittbull loves it
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 2, 2026
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Verified Purchase
CA
Draper, US
★★★★★ 1
Our dogs hurt their mouths chewing these bones
Color: Purple & Blue
I don't do a lot of reviews because I realize many are objective opinions. However, in this case I felt it was necessary to warn others. Our dogs are aggressive chewers. Their last rubber bones (not these) which we've purchased before, and recently purchased again, were destroyed quickly. Chunks of rubber came off the ends. Since those didn't hold up like they used to, I found these harder bones hoping they would last longer. They were able to gnaw into the hard plastic within a few minutes. This created sharp edges that cut their mouths. When I saw a bit of blood on the bones, I took them away from the dogs and threw them away. I wondered why they quit chewing on them after being so excited at first. Also, these are hard enough to damage a tooth.
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Reviewed in the United States on December 6, 2025
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Verified Purchase
Patricia Smith
Cuba, US
★★★★★ 2
Pups have shown zero interest in these toys….
Color: Purple & Blue
I would agree that these are indestructible being neither of my dogs have shown any interest in these at all. At this rate they should last forever…
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on April 10, 2026
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Verified Purchase
Cosmicethos
Pawtucket, US
★★★★★ 4
Durable but losses interest
Color: Purple & Blue
My dog is an aggressive chewer. She was interested in this toy while it was new, but soon after lost interest. Good news is although it took a beating it did not break or splinter. If soppy toys are disposable in your house, give it a try.
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Reviewed in the United States on June 8, 2026
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Verified Purchase
Lazychick
Carnegie, US
★★★★★ 5
Great for Excessive Chewers and Eaters
Size: Large (Pack of 1), Product Packaging: Standard Packaging
I decided to get the Kong Extreme toy for my then 9-year-old dog in Sept. 2010, after her older sister passed away a few days before. I figured we both could have used the distraction. I learned ages ago that most toys couldn't hold up against my two Australian Cattle Dogs, since they didn't just happily gnaw on things, they'd try to eat it. In fact, they tried to eat a number of things, from fabrics to meticulously eating the lining off tennis balls and soft balls. Nothing was safe, especially against the youngest, who has some OCD issues. I'd be lucky to see a tough toy last a day, much less a month. Like the rest, I didn't think this toy would stand a chance, but it's still holding up well almost a year later. My dog isn't a strong chewer, like a doberman or pit, but very meticulous. She and her sister would go at something for hours if you let them, until nothing was left. Because of this, I also need to choose soft toys, rather than something hard, because she'll wear her teeth down if you let her. Fortunately, this manages to stand up to her obsessive chewing, but it also doesn't wear the teeth down, which I love. I'm thinking of getting a new one, even though the current could probably last another few months. I'm just now seeing some wear along the seams, despite her every effort to conquer and destroy it. I'm mainly getting it just to be on the safe side, so that I don't risk it falling apart while I'm not watching her, and just for the sake of cleanliness. These are extremely durable and easy to clean. They do have a strong odor when you first open them up, but it fades relatively quickly. I let ours soak it in hot/vinegar water for a while, then rinsed it well and left it out in the sun for a few hours. Seemed to help a little. They can also be loud when dogs chew on them, which can be annoying if you're trying to watch TV, but I find it well worth it, even if my partner doesn't agree during football time. I love the fact that these toys bounce unpredictably, although I would be careful around furniture if you plan to bounce it off the floor or toss it. I got into the habit of using it down our long hallway, referring to it as Dog Bowling, which she loves. She also didn't need food as incentive to get into it (just me playing with it and making it out to be a big deal), which is great, since that just means less cleaning and less weight gain in my book, although I do put treats in it now and then, if my partner and I are leaving the house and plan to be gone awhile. My dog's around around 30 lbs. and is medium sized, but has had no trouble tackling the larger-sized version, which was the only size available through Amazon at the time. I may get the medium-sized toy soon, just because she's reaching 10 and she'll go at it for ages. This is a great toy for obsessive chewers in particular, and I highly recommend it to dog lovers. I just wish we'd found out about them sooner! I'm also happy to report that she has stopped chewing on random things), like blankets and clothing, as much as she used to. If she does start up, it's because she can't find her Kong. I may also get the bone version and will review on that if I do.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on August 28, 2011

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